The shift solenoid usually gives a problem on the 2-3 and 3-4 shifts, but that doesn't mean that you can't have a problem on the 1-2 shift. The throttle valve adjustment can give you a delayed shift and the throttle position sensor(TPS) can also give you shifting concerns, although the TPS usually affects the torque converter lockup. You may have codes in the PCM that can be checked to help with your diagnosis. A scan tool that can read data would be very helpful in pinpointing the area to look. If you don't have one then all you can do is replace parts until you find the issue. Start with the throttle valve adjustment since there is no cost involved with this.
Ok, I have already verified the TV cable is the correct length and operating correctly. I have also checked the trouble codes via the "key method" and have nothing corresponding to the transmission (just an O2 sensoer). This system is an OBD-I system with a seperate Transmission Control module. Will the codes show up using the "key method" or will i have to use a scanner to get the codes for the trans?
Also, one more thing, would it be possible for an incorrectly adjusted band to cause these problems?
Since the TCM is separate, you will need a scan tool to read the codes if there are any. You could adjust the bands just as a process of elimination, don't usually see much problems with them.
If you do a very light, easy acceleration do you experience the same kind of problem?
Yes, The problem is experienced regardless of light or heavy accelleration. The difference in acceleration does determine the RPM in which the problem occurs. Heavy acceleration will cause the problem at a higher RPM, lower acceleration will cause the problem at a lower RPM, but it only happens between 1-2 shifts