As I remember the D-3, I believe that the heads are connected to the door, so they move every time the door opens or is closed. Thus, the extra movement makes them come out of alignment more often than other small recorders. Based on your cursory description, I think it is a head alignment issue.
I suggest the following:
1. Unless you LOVE the small size of it, but want to remain cassette analog, but a d-6 or d-5 to replace it. (You can get those cheap these days). A D-6 is not much bigger physically, but I think a much higher quality unit. As I remember talk amongst Dead tapers when the D-3 came out "It's half a D-6".
2. If your budget is a bit bigger, look into the CHEAP 24 bit recorders out these days. They are even smaller than a d-3. Plus, you don't have to buy tapes for it!!
I would not spend the $$ getting it fixed/calibrated. You can use your cash more effectively elsewhere.
Good luck!