Mediocre Thesis Topic. Does this Hurt my Reputation Just curious as to the effects of publishing a mediocre PHD thesis:

After sitting down and taking a cold, detached, look at my thesis topic, I realized I was given a pair of coobook-style problems, i.e., in order to answer the questions I was given to answer, I just need to go over a list of requirements and see if the general results apply to my specific problems. Instead of research level, the problems I was given look more like exercises at the end of a book; a graduate-level book, but still, cookbook.

Question: Once I am done with this, which shouldn't take more than a few months, how will this look to anyone going over the thesis? Since I will be having some extra time, I am considering doing some extra research and tacking it into the thesis. Is there something else I can do?

I suspect my advisor may not have  a very high opinion of me and thought I could not likely handle anything more complicated. This itself brings issues as to the recommendations I may receive when someone asks my advisor for a recommendation.
A PhD is documentation that you can do your own research.  You don't have to take what you're given.  That said, maybe your advisor considers the "toy problems" a warmup for more advanced research?  You should talk to your advisor and also to other faculty members you trust.  Let them know that you are concerned your topic may be weak.  Perhaps they will have some ideas on how you can make it stronger.  Depending on the outcome of these discussions, you may want to shop around for a different advisor who is a better fit for you, both in research interests and personality.  The key is to take charge of your own dissertation.