Mechanical jellies: What could possibly be causing this automatic transmission problem?

The car: 2000 Subaru Legacy Outback wagon

The issue: Automatic transmission doesn’t want to go into Drive immediately and it’s getting worse. It will shift straight into reverse and once it does slip into a forward gear, there are no further shifting problems until I park again. Gears shift smoothly when driving, no weird noises or hitches and no problems starting up from a stop at a light. The transmission fluid is full, though it’s probably been at least a year since it was changed.

Please tell me this sounds like something easy and inexpensive to fix.