I've never used OCaml, so I'm curious to what exactly happens, and if language design can prevent that.

If I download a random project and delete the interface files, will that be enough to see issues, or is it something that happens when writing new code?

If you delete your interface files and then change the type used when calling a function it can cascade through your program and change the type of the function parameter. For this reason, I generally feel function level explicit types are a fair compromise. However, making that convention instead of required (so as to allow fast prototyping) is probably fine.

Just require it for public functions. Your own code can be as messy as you want unser the hood