Simple answer, none and all of them. None remain 100% compatible; all remain broadly usable.
There are a lot of books released for Mongoose Traveller 1st edition (MT1e), so I couldn't put together a list as requested solely because it would have to be pain-stakingly researched to give you an accurate answer.
Right from the start of the open 'playtest' last year, Matt Sprange noted on the Mongoose Forums that while the core principles of the old system would remain, the design team would not let any of the old material hold them back from making changes. If a change would make the game better, they'd make it - backward compatability be damned.
On the other hand, they were not setting out to intentionally invaidate any of the old material - and if you own one or more books from MT1e - or, indeed, other versions - you will not find them rendered worthless. You will need to do some legwork understanding the changes and deciding what to keep and what to go with.
Broadly speaking, the stats for people and places have remained the same. The crunch for ships and ship weapons got a bit of a tweak as did the system for large scale battles. World building has remained the same as MT1e; character creation, especially skills, has undergone some slight adjustment.
As I say, you will find the old books generally usable - but Mongoose did not hold back from making changes in MT2e to 'make it better'.