Does anyone else think it might be helpful if the players who have no trade clauses or are 10/5 guys have a list somewhere of the teams they would approve trades to? It's quite annoying/tedious to have to go to each team individually and offer a trade to see if the player will choose to invoke his no trade clause. I feel as if this could be a simple addition that would also be very practical. If someone knows of an easy way of checking this out now I am all ears. I know usually a player won't go to a team with a worse record but I also know that's not always the case. Thoughts?

Im with you on this, However, HBD tries to mimic real life as much as possible, and this happens quite a bit. Mostly doesnt get reported. most recent example, Derek Lee vetoed the trade to the angels, after the cubs and angels had worked everything out.

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i just tried trading one of my guys with NTC to a team that has won there division 4 straight times and this year the team is 26-27 a few games out. But he would accept a trade to a team that has only made the playoffs  1 time in 22 years but this year is 30-23.  Its quite confusing trying to figure out what they really want and will accept

Rule of thumb: they will accept a trade to a team that has a better record than yours.  They will refuse a trade to a team with a record worse than yours.

If it's before game 27 (I think) of the regular season, then it reverts back to last season's record.

Waiver wire order. 

Yeah, same thing.  Unfortunately, there's no easy way to see the waiver wire order (other than where your team currently is) at any particular point in time without going to look at standings and team records and figuring it out yourself.