The Rest of Your Mouth
The rest of your mouth need not be a big bother to you.  But, you should have a dentist and/or doctor look at the rest of your mouth at least once a year. 
Your tonsils, if you still have them can become inflamed, infected, and contribute to sleep apnea.  They can also be responsible for really bad breath.  Salivary glands can becomed clogged.  Tissue shedding can happen.  Ciggarette and cigar smoking will cause red dots to form on the palate that are called nicotine stomatitis.  Chewing tobacco will cause the cheeks and gums to become leathery and wrinkly.  Also, oral trauma can happen from frequent cheek and lip chewing.
I can make a list a mile long.  Suffice it to say, a lot of things can happen in there.
All of the tissue in your mouth can be susceptible to changes.  Those changes can become cancer.  Any white lesion should be looked at by a physician, dentist, or oral surgeon.  In fact, if your doctor or dentist finds something he deems "suspicious", he will probably refer you to an oral surgeon to have it removed and biopsied. 
This is not the time to freak out!  These tissue changes are rarely anything.  But wouldn't you rather know that it is nothing?  Yes, you would, trust me. 
Pay attention to any tenderness that lasts for more than a few days or any sores that keep coming back or won't heal.  You also want to watch for unusual swelling.