Been taking my dt2 250 out for short rides on the weekends. No more than 3-5 miles per session,

I've noticed that it's having trouble shifting gears.This seems to be happening more frequently but, when I try shifting to 2nd, it’ll shift to neutral. Then I have to shift back to 1st and try to get to 2nd from there. I may have to try this 5-8 times before it shifts to 2nd and onward. Its also doing this when I try and shift from 3rd to 4th, though not as often as from 1st to 2nd. 

Could replacing the clutch plates fix this?

Also the clutch lever is pretty heavy and the friction zone fairly small. Could it be a clutch cable issue or adjustment needed?

Or is this problem indicative of something wrong with the shifting gears (I hope not).
 

First thing I'd check is if the detent plunger and spring is in place... many get lost when someone removes the wrong plug to drain the transmission.

Have you dropped it & possibly bent the adjustment screw on the change arm in behind the clutch.
But i'd go with Mark's idea before anything--plunger on the left underneath--has spring pushing it too.
Foot not side pushing the lever into the magneto case during changes.
Sit it in 3rd gear & then by hand feel the amount of lever movement up then down [below & above] the central position the return spring holds it at & see if the movement to connect the next pin is about equal up & down or if one direction is touching the pin then extra travel the other way to get to the up change pin. Has to be third gear or fourth gear. Actual second would be ok just thinking, but not first or fifth, or neutral.

Thanks MarkT and RT325,
Confirmed that the spring and detent plunger are still in place - though I dont recall what sequence I installed the spring and plunger... I think I had the plunger above the spring.

Also the bike has never been dropped (at least since I've owned it).

Its been shifting fine for the last month up until a couple weeks ago. I dont think ive made any adjustments that could potentially cause this - aside from popping off the side cover of the front sprocket.

Does the adjustment screw area of the cover need to be greased?
 

I'm no expert in these matters, but when I took my detent spring out it crumbled into three pieces in my hand. If you wind up checking the detent, I would make sure the spring has some "spring" in it.

If it has been used off road, and the gear lever has been hit hard, then the gear change mechanism stop peg can get broken out of the crankcase.

Generally, when this has happened, the gear lever action will feel a bit weird, and the lever might not return to the same position every time.

It can usually be repaired with TIG welding, after the clutch cover, and clutch has been removed. Not that difficult a job, but quite fiddly.

Nothing to do with problem but Yes you can grease the actuator by turning it out & removing to grease.
Good idea too which is often overlooked.

I identified the problem that was causing the shifting problem I was experiencing... its quite comical actually. First I tried different adjustments with the clutch cable tension. After that didnt work, I bought a replacement clutch cable as I thought it may be fatigued. And if that didnt work then I was going to open up the clutch pack and replace the friction plates.

Before replacing the clutch cable, I wanted to check the oil level in the crankcase. As I go to remove the oil plug, I feel that the dipstick portion is caught... I shift the bike into first and it comes loose. It turns out that the rubber dipstick was arching inward towards the gears (I suppose from the angle of the bike leaning on the kickstand) and getting caught in the shifting gear, thus causing the shifting problem I initially described 

After straitening the dipstick and reinstalling, I immediately took the bike out for a ride, and what do you know... She shifted with zero hiccups during a 45-minute ride.

This problem caused me so much grief, but I'm glad it turned out to be such a simple fix.
Hopefully this post can help someone else in the future 

That's a new one I hadn't heard of before! Good job figuring it out!

Well i'll be $%^&. There's always something new to lodge in the memory bank.
Great you found it before we had you dismantling it & finding nothing.
I might be wrong but thought the early DT1's had a steel probe set into the cap which wouldn't bend.
Looks like i 'am' wrong, just googled the part number for "68 & still looks rubber.