Okay, regarding universal salvation, here are my main problems with it (and most of these will overlap with the others):

1. It is based on the idea that the all who are in Adam become the all who are in Christ (from Romans 5 - see below). But I don't see this at all, I see Paul making a contrast between Adam and Christ. Everything born of Adam dies - everything born of Christ lives. All in Adam are sinners - all in Christ are righteous. In reality, nothing of Adam goes into Christ for it is a new creation. It has to do with headship: the first Adam vs. the last Adam; the first man vs. the second man. It has to do with birth, and therefore, inheritance. No one in Adam inherits life, but all in Christ do. Later in Romans (and also in Galatians), Paul refers to a distinction between the sons of Abraham as being either through Isaac or Ishmael. All through Isaac are the children of promise and free while all through Ishmael are NOT of the promise, but slaves.
2. It stands too much on a reaction to modern Christianity's redefinition of faith. There is this tendency to pooh-pooh the distinction between believer vs. non-believer. If you follow all of Romans then you will notice that Paul describes believers as those who have been taken out of Adam and put into Christ, but he doesn't suggest that as being true of those who don't believe. But this teaching assumes that this is just another wall put up by legalism and in doing so overlooks much of the miraculous nature of faith. For the point of calling a person a believer was never made to suggest that a believer is somehow better than an unbeliever, it instead designates the recipient of the miracle of the life of Christ as having nothing to do with any merit.
3. This teaching says that all are saved or redeemed and have Christ in them and just don't know it ... yet. The fact is that none of the apostles said things like this. Instead, John, Peter, Jude, and even Paul speak many times of those who do not have the Spirit and have no life in them and stand in condemnation. I've listened to those who hold to this teaching and I have observed some really out of context explanations and sometimes plain rejection of the passages in question based on historical tampering, etc. Interestingly, they don't suggest that of Romans 5 or 2 Corinthians 5. :)

Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned for until the Law sin was in the world, but sin is not imputed when there is no law. Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come. But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification. For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ. So then as through one transgression there resulted condemnation to all men, even so through one act of righteousness there resulted justification of life to all men. For as through the one man's disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous. The Law came in so that the transgression would increase; but where sin increased, grace abounded all the more, so that, as sin reigned in death, even so grace would reign through righteousness to eternal life through Jesus Christ our Lord. Romans 5:12-21

For the love of Christ controls us, having concluded this, that one died for all, therefore all died; and He died for all, so that they who live might no longer live for themselves, but for Him who died and rose again on their behalf. Therefore from now on we recognize no one according to the flesh; even though we have known Christ according to the flesh, yet now we know Him in this way no longer. Therefore if anyone is in Christ, he is a new creature; the old things passed away; behold, new things have come. Now all these things are from God, who reconciled us to Himself through Christ and gave us the ministry of reconciliation, namely, that God was in Christ reconciling the world to Himself, not counting their trespasses against them, and He has committed to us the word of reconciliation. Therefore, we are ambassadors for Christ, as though God were making an appeal through us; we beg you on behalf of Christ, be reconciled to God. He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him. 2 Corinthians 5:14-21