The concept of germs mutating to become resistant to various drugs is actually the least of our worries. There are only a very few microbes that are known to cause diseases that can do this on a regular basis.
The BIGGER issue is that we are killing off all the germs that can be killed off with antibiotics and so forth. Take Methacillin Resistant Staphylococcus aureus (not sure if I spelled it 100% correctly). This is commonly known in the media and healthcare as MRSA. This is not really a mutated form of S. aureus. It is just a strain that is resistant to Methacillin's. The reason this has become so common in the hospital systems is because we can kill off many of the other Staphylococcus bacteria. This leaves only MRSA to multiply and reproduce. There is no need for it to compete for nutrients. Heck, S. aureus can naturally be found on the skin of healthy humans.
Another microbe that, suprise suprise, often times found in the hospital is Clostridium difficile. This is usually refered to as C. diff. You can find this microbe on pretty much ANY SURFACE of a hospital. If you have stepped foot into a hospital, you have come into contact with it. So, why does the normal person not have infections from this microbe? It is because we have naturally occuring bacteria in our intestines that prevent major colonization of C. diff. BUT, when someone has another microbe colonization, say with MRSA, the antibiotics given are so strong that they kill off ALL bacteria, even those that are healthy and occur naturally. This gives C. diff the ability to colonize and create havoc in the intestines.
Basically, IMHO, there are times to use antibiotics and so forth. But I will disagree with Neosporin or Band-Aid about EVERY cut needing it. No, not every cut needs it. So your finger is a little red, guess what, that is normal. It is part of the healing process.