From your description it sounds like the saddle (the plastic strip in the bridge) could have become worn by string wear and tuning (the string acts as a sort of file against the plastic or bone material, cutting itself a deeper groove and causing slight intonation problems. The same could be true of the nut for similar reasons. Either could be recut, or if necessary, replaced rather easily.
With some minor and inexpensive adjustment from a good guitar technician or repairman and a new set of strings, there should be an improvement. If you like your guitar it is certainly worth it. If you are handy and would like to try to do it yourself, you'll need a special needle file (Stew-Mac sell them) and Frank Ford's excellent site gives very good guidance on how to accomplish the job.