It's been ages since I studied Hamlet, but I think two major contradictions are
- early on, (line 8 I think) Hamlet says that dying is preferable to living, but later discusses at great length that people bear awful tragedies and conditions in life, and must do so because they fear the afterlife. So is death good or bad?
- Hamlet talks about no traveller returning from the afterlife, yet he is visited by his father's ghost. So, do travellers return or not?
Bard.net is a good resource if you're struggling.