Should I put my marked assignments online?
In my alma mater, this is indeed common. The student representatives actually maintain a repository of exam answers and assignment solutions for all large classes. Contributing to such a repository seems better than putting it online on your own web page or GitHub, because you need to think about how the students coming after you actually find your material.

As for other implications: the only thing that I can think of is that lecturers are sometimes not all that happy about this practice, as it makes re-using assignments from previous years more difficult. However, that's not actually that big of a deal, as most lecturers will assume that the solutions to re-used assignments are somewhere out there anyway, and adapt grading respectively.