I have a 97 Accord with 238K miles and recently I've noticed that when I shift the car from park to D4, sometimes it will take it a couple of seconds or so to "engage" and take off. What causes it to hesitate like this? Thanks!

 

Possibly a pressure drop issue.
When was the last time the fluid was changed?
If never, change it. There is probably a build up of material in the sump that is blocking the sump.

 

This is the same problem I have. And in addition, when it does shift into D4, there is usually a big jolt. There is no D4 blinking light and the car engages fine once you drive away, and for the rest of day. Before I changed 4 qts of fluid, I had no trouble at the end of work (when the car has sat for 8 hrs), starting the car and shifting into D4. But now, I get the delay, so changing the fluid made it a bit worse.

I do find that warming the car up for 3' in the morning, and in particularly, revving to 2000+ rpm for several seconds cures the problem. Right after I do this it shifts into D4 immediately and softly.

Because the tranny shifts fine otherwise, 'guess I have to put up with it and hope it hangs together until I can rebuild it.

 

Changing the fluid reduces the delay. If the transmission has a lot of miles there may be a buildup of clutch material in or near the pickup, blocking flow. Drain the old fluid, and refill.