No one knew the answer. However, we do have a Shakespeare buff in our department, so she was not about to let this question go unanswered. The question was asked yesterday. Here is the answer she gave us this morning after researching last night:
Here's the answer to Dan's question about why Shakespeare would sometimes say "seems" and sometimes "seemeth." In a nutshell, it's really about the shift from Middle English to Modern English forms. Shakespeare is considered Early Modern English. The -s ending gradually replaced the -eth ending. Shakespeare wrote during this shifting time, so he was free to choose based on his preference for emphasis and scansion.
Here's more info:
So now you know too!