Here's the description of the "strict" compiler option that goes a long way to make your program more reliable :
"Enable all strict type checking options. Enabling --strict enables --noImplicitAny, --noImplicitThis, --alwaysStrict and --strictNullChecks."
Some of the soundness issues are by design (making directly overlayed JS code reasonable to type/interface with), some are due to 'taking too much time/design complexity if implemented'.
I won't go into them one by one, but you can jump into most of the issues here to get a sense:
https://github.com/Microsoft/TypeScript/issues?utf8=&q=Sound...
https://github.com/Microsoft/TypeScript/issues?utf8=&q=unsou...
I won't take a position on the matter other than to say that it's a tricky balance and the TS team are at the very least extremely clear in saying that you should not be looking for a high degree of soundness here (JS interop is a higher priority).
If those things are important, I would recommend Scala.js or PureScript or... anything more self contained (and remember that they're still ultimately dynamically typed on the JS boundary, just not inside the language).
Here's the TS team explaining their position themselves:
https://github.com/Microsoft/TypeScript/issues/9825#issuecom...
https://github.com/Microsoft/TypeScript/issues/13003 (not the most cordial commenter unfortunately)
Overall though, getting bitten by the unsoundness is fairly rare , imo.
I think I wrote a lot of code assuming that the type checker was sound and could check my abstractions, only to find that it wasn't and it couldn't.
If it were more sound, I would rely on the language to do more checking.
I don't get bitten as much any more, but I'm pretty sure that's mostly because I know what tradeoffs the language is making and I use other mechanisms to ensure safety.
And no, Flow is MUCH more sound, I have worked with both. Flow's limitations tend to be false negatives (code that should ideally work does not compile as is) whereas Typescript's are false positives (fails to detect type errors).