Electrical problem or mechanical problem?

We own a 1996 Automatic SOHC Neon with around 160,000 miles (haha beat 100,000). Recently (especially when its damp/wet out) it will shift erratically and the speedometer goes crazy. Like you will drive it and it will go from first to second ok but then around 25mph it will try to shift into like 3rd and it will struggle to take hills. also even sitting in park the speedo will go crazy. it will whip up to like 80 mph and just wave around. usually if you drive it 20+ miles or let it idle for around 20 mins it will all smooth out (Sometimes when it idles it will race till everything works out). Also when this happens the check engine light won't come on no matter how crappy the engine runs. Ive checked for corrosion on the wiring and it all looks clean. all the fluids are topped off and the oil was just changed around 30 miles ago. Any ideas where to start?

Im wondering if the bad idle could be caused by a bad O2 sensor and maybe the PCM isn't picking up on it and could the erratic shifting and weird speedometer be caused by a bad Speed sensor?

Okay update just took it to get gas and on the way back check engine light popped on. got it home and checked the codes.

12 - Problem with battery (its cause i had to remove the batter to hook back up the battery temp sensor)
42 - Fuel Pump relay or auto shutdown relay control circut indicates an open or shorted circuit condition
21 - Problem with oxygen sensor signal circuit
42(again? i checked the codes twice and it comes up twice)
55 - end of codes

any ideas?

Code 21 - Check your wiring to your upstream O2 sensor and make sure its not frayed. Also check the sensor itself, may need to be replaced.

Code 42 - relay may need to be replaced. Swap the horn relay with it and see if the horn works. If so, then it's OK.

Ok today was a nice warm dry day so i got under there and looked around. Looking at the Upsteam O2 Sensor i discovered it was partially unplugged so i plugged it back in and will have to see what happens. also i took a look at the speed sensor and when i unplugged it quite a bit of tranny fluid was in it so i think it was kinda shorting it out so i cleaned that all out and ill have to see it the speedometer is normal now. Also Checked the relays and they were ok. Reset the PCM and so far the check engine light is out but ive only drove it for about 30 mins.