looking for an answer to this puzzler

Probably grasping at straws, but I wonder what the thermometer reading would be if the fellow lowered/raised the oven rack and checked the temp.  Might there be cool spots in the oven?

Also, is the oven clean?  Dirty ovens will cause uneven heating - according to Alton Brown.

Does the oven door seal properly?  Leaking ovens make poor baking environments.  He might also want to check the recipe.  Excess baking soda can cause sugar to do strange things in baked goods.

Oven controls, especially on older ovens, are quite easy to adjust.  Most of them require little more than removing the control knob, looking at the mechanics and adjusting it so that the control knob reading agrees with the actual oven temperature as read on a good quality oven thermometer.  Nothing needs to be removed except for pulling off the control knob as you might ordinarily do for routine cleaning.

Here's a step by step that might help:

http://www.ehow.com/how_8260_check-adjust-ovens.html

Does it heat?  Remove all shelves and pans and bottom of oven if it easily comes out.  Turn on the oven while resting your hand on the bottom of the cold oven.  To see if it heats up.

Dial confusion...  Many new (picture only) oven settings can be confusing, what are they and which one is being used.  Visual guide important.  (Suspect lower heat not in use.)

Ovens (both electric and gas) work by cycling back and forth from a little below the desired temperature to a little above. For example if you desire 350F, your oven might drop to 325F, then turn on, then go up to 375F, then turn off, then drop back to 325F, and so on 'round and 'round. How is this relevant? To make it work, one should  look at an oven thermometer many times and figure out the middle. If you look at an oven thermomemter just once, chances are you'll catch it near one end or the other of the cycle, and get a misleading idea of whether the oven is too hot or too cold. (Reporting an oven is 25 degrees off sound more like not using the thermometer correctly than a true oven problem.)

That said, it nevertheless does indeed sound like there's some problem with overheating or underheating or markedly uneven heating. The fact that "baked good are not burnt" doesn't surprise me at all, as only an oven that's a whole lot farther off would routinely burn things; the user will notice funny problems like too little or too much rise, thicker chewier crust, blowouts, etc. long long before anything is burnt. And given how the temperature sensor and the controls are made (at least on electric ovens:-), it's quite unlikely that they're "going bad". It's not impossible, but it's quite unlikely. More likely the oven will work perfectly right up to the point where all at once it goes way way off.

So what might cause sudden oven temperature problems? Some ideas are noted in other posts, including a broken spot in the door seal and something else such as a pan or a piece of foil left in the oven. Another idea is something caught around the temperature sensor. The culprit may be a piece of tinfoil, or a crusty sheet of oven gunk. The temperature sensor is usually either laying right along the edge of the oven in one of the top corners, or covered and out of sight. If something that was baking (like a pie?-) ran all over the oven and dripped horribly, some of the drips might have run behind the cover and are now messing up the temperature sensing.

(Also, on newer ovens with a covered bottom element, lining the bottom of the oven with tinfoil is a no-no. Doing so will likely mess up the temperature and will probably partially melt the tinfoil into the bottom of the oven so you can't get it off. The "right thing to do" with older ovens with an exposed bottom element is "the wrong thing to do" nowadays.)