Is a 1935 US 2 dollar bill legal tender?

Except for the fact that the U.S. never issued any $2 bills in 1935, yes, old $2 bills are still legal tender.

Contrary to popular misunderstanding fed by various internet rumors, the US still prints $2 bills, the denomination has never been discontinued, and the bills have never been withdrawn. In fact, you should try to get and spend $2 bills because they save money for taxpayers. Every $2 bill that's spent instead of using two $1 bills means that many fewer ones have to be printed!

The U.S. has never demonetized any Federal Reserve Notes, U.S. Notes, or silver certificates so technically you could go to a bank and ask for change for, say, a 1918 issue $1000 bill. Of course many (but not all) older bills are worth a lot more to collectors, so it wouldn't make too much sense to spend one at face value. That $1000 bill, for example, would be worth 5 to 8 thousand to a collector ...