The Mass
The mass is just an order of service and like any other denominational order of service is just a sequence designed to keep an order in a church service.
It is purely an administrative thing so is neither correct or incorrect.   As The Bible does not tell us the order to use in a church service, any order of service can be correct except where it is idolatrous in part. Some or all of the individual activities in the actual service may be incorrect and these need to be examined separately using the two tests.
If the individual part of The Mass is not in The Bible then it will need to pass the second test.  I cannot see any part of The Mass that is actually in The Bible so all will need to examined according to the second test.  
Remember, that the activity of reading of The Bible in the format it is done in the Mass is not in The Bible but the contents of the activity (The Bible) is so this would pass the second test.  Do not confuse the authorisation of a part with the activity in the part of the Mass.  The activity itself may not be in The Bible so that it is needs to pass the second test but the actual contents may be confirmed or condemned by The Bible so it would fail the first test.
If it a part of the Mass passes both of these tests then this individual part cannot be criticised.  If it passes only the second test then it cannot be a requirement of salvation and is peculiar to the church practising and its observance cannot be enforced on others as it is not Biblical Doctrine but only practice of that particular denomination.
That which is the main part of The Catholic Mass and other denominational services is Communion and as the Catholic celebration of it (and similar celebrations of it)  cause the most problems to non-Catholics, I will exam this in the next section.
Communion
The comments made here can apply to all denominations not just The Catholic Church
Communion, as practiced by a denomination is so far removed from the communion practices of the early church as to be unrecognizable as communion as instituted by the early church.  The format of  the communion service is not described in The Bible.  The communion service in The Bible was a collection of thing’s  not just the bread and wine which has taken over communion to the neglect of the other parts.
As the format is not described in The Bible the communion service format cannot have the first test applied to it.  However, some of the activities are in The Bible and these are lacking from modern communion services so these modern services are not the way God instituted it.
It was originally a fellowship (communion meal) and not just a remembrance of the death of Jesus.  A meal in which people shared what God was doing, encouraged and helped each other and ministered to each other.  It was the totality of the experience and not just a small part of it.  But as churches got bigger a substitute had to be found as this format was impractical so all was dropped but the remembrance of the death of Jesus.  Even then what was said and done was not done the way Jesus did it but became formalised and standardised so it would not be done ‘incorrectly’ anywhere.  What is done now is a ritual designed to be standardised so it is performed the same everywhere in a denomination and is far removed from what Jesus and the church originally made it to be.
In a sense it is not Biblical communion but a man made copy for expediency in the denominational setting.  As such one should perhaps not even try to compare it to the early communion services and just use the second test.
Jesus ascribed no magical significance to communion and it was not his body but representative to what was going to happen to him.  It could not have been his body or shed Blood, as He was still alive and to ascribe any magical significance to it as transubstantiation does is incorrect.  His reference to His Body and Blood  could only have been symbolic because it was a sign of what He was to do and not a sigh of His physical presence.  As he was still alive when he declared it to be his body it could only have been a representation.  The same with the wine.  It could not have been his blood, but only representative of it as He was still alive.
Communion as it was practiced in the early church was a joyful time remembering and sharing what Jesus had done for them.  It is not the sombre, serious event that is held in most churches these days.
Instead of a ‘love’ feast as it was in the beginning it has been turned in to an almost sombre, mystical event by the church.  Instead of a joyful celebration of what Jesus has done for them.  It has been turned in to a sacred, holy event that drives away joy and thanksgiving. Instead of being a group event of communal worship, it has been turned into an individual experience and a memory of His suffering and not of what He has done for you or the reason He went through Calvary for you.
Nowhere in the New Testament, is it anything but a meal and nowhere in the Bible is any other way of celebrating communion mentioned or recommended.  It could be argued that the communion really occurs at the Sunday meals after church as that is more in the spirit of the original communion than what is practiced in churches.
The presence of Jesus in the Eucharist
The belief that Jesus is actually present in the wine and bread is a belief that is not in The Bible.
A person can believe in something that is not true providing it does not become an idol or displaces the Lordship of Jesus in any way.  There is no problem with the Catholic belief that The Bread and Wine are the literal body and blood of Jesus providing it does not displace Him as Lord or causes a weaker brother to sin.  If that is the way they interpret it then until they are shown and understand any truth they need to know God will not hold it against them.
Transubstantiation
It is not in The Bible so the first test cannot apply and only if it passes the second set of tests is it acceptable as a practice.  As it is not in The Bible it cannot be doctrine as God alone can mare true doctrine.  As it is not doctrine it can only be observed by The Catholic church as a practice and not is not enforceable on others.  As long as the host is not worshipped in its own right (in which case it replaces Jesus and is idolatry) but as a representation of Jesus then there cannot be anything wrong as it becomes a aid to draw closer to Jesus..
If the effect of the Eucharist on Catholics is to draw them closer to Jesus the question arises how can it be wrong?  If it passes all the second tests it becomes a practice that can be performed but cannot be made into a doctrine as it is not in the bible.
The major problem with the Eucharistic ceremony is the lack of love that those for it and against it show to each other.  In this is sin.  The other danger is to elevate the ceremony to a point it displaces Jesus as the object of worship so that it becomes idolatry.  These are the dangers and as usual Satan uses something that is not of eternal significance to cause problems and possibly people to lose their salvation through unforgiveness and judgmental critical attitudes that are not repented of.
If we were to be judged by God for all our errors of doctrine or erroneous practices no one would get to heaven.
If the communion order of service passes all the sections of the second test there is nothing wrong with using it .  But when it is made doctrine (which it cannot as it is not in The Bible) or fought over in a loveless, judgmental, critical attitude then it is a problem as it breaks the law of love and probably should not be practiced in the way it is.
If you cause your brother to sin you are in trouble with God and in this is the danger of The Eucharist that for centuries it has been made doctrine incorrectly and brother has caused brother to sin over it.  Accordingly, while it is not an erroneous practice in itself (but one that can lead to idolatry) it is one that divides and for this alone is probably a failure of the law of love.  If you love your brother you will not do anything that causes them to stumble, unless what you do is Biblically correct in which case you must be careful the way you do it is an expression of love and humility and not legalism.
Fellowshipping in mass and communion
Can Catholics and non-Catholics  attend mass or denominational church services together or share in communion or the Eucharist together?
Where there are items of common faith there are no problems, The actual order of service cannot be a problem as the Bible is silent on this and as long it passes the second test no one can have any problem with them as God does not.
Where Catholics or denominations  have practices not in the Bible then it’s up to each individual to do join in them and no church has the right to ask or force any one to do these practices against their will.
If the practice is not idolatrous and not in The Bible there is no reason why you should not partake in it.  It would have passed the second test. If it is idolatrous but is done out of ignorance or lack of understanding of the truth it would have failed the second test but then they are not sinning  as they are doing what they know to do and not what they do not know to do.  However you would sin if you did it as you know it is wrong and you should humbly explain why it is wrong to them and then walk away and let The Holy Spirit deal with them after the discussion is over.
As long as communion is used as an aid to worship of God and/or an expression of their love for Him and is not worshipped in itself then there is nothing wrong with this ceremony as it passes test two but it becomes purely a Catholic practice, is not doctrine and cannot be enforced or expected of those outside the Catholic Denomination.  If the practice passes the tests it should also not be criticised by those not practicing it as it does not contravene The Bible in any way.
In Summary
The Mass structure or denominational service structure and communion  as practised by most churches these days are not in the Bible so if the practice passes the second test no one can criticise what is or is not done in them.  However, doctrine cannot be built on these non-Biblical activities and to do so in wrong.
Doctrine can only be based on The bible and these are not in The Bible.