My 96 toyota tercel, automatic, 1.5 liter runs pretty good but hesitates to shift from 2nd to 3rd. if i let off the gas and drop the rpms alittle it will shift fine.other times i have to let off the gas a couple times before it will shift up.fluid was a little high so i drained a little , didnt seam to change though. also, i can hear the band slip a little when i put it in reverse and give it a little gas, usually when its hot.we've only had this car a couple of days, any help would be appreciated.

I tried the DIY service and repair manuals from a website and it actually helped
me repair transmission problem in my ford explorer. it wont move forward or reverse, engine is good both solenoids for forward and reverse work.
I don't have much technical knowledge but I just followed it step-wise, and works perfect! got it from www.reliable-store.com

Sounds like the syncro may b damaged. Typically a clutch problem would be noticeable in all gears, especially shifting into reverse when vehicle is running but not moving. Try giving a 2 count for engine RPMs to drop before going into third to see if that helps. Won't fix anything but might cut the grinding sound. Till you can get the tranny fixed or replaced.

TPS throttle position sensor might need adjustment or the catlic converter in the exhaust needs replacing as its not leting the exhaust out freely.

rattling noise from front, first rule out any loose heath shield check exhaust system, and also your engine mounts when given gas your engine shifs under torque and when you let off the gas to shift engine moves back(no load, torque) if loose or broken mounts may cause interierence on moving parts(binding). do this firts good luck

Why are you shifting from 2nd to 3rd gear ? is this a standard or automatic? If its a automatic its normal for the torque converter to catch up with the speeds of the tranny. To save the life of your tranny try to let the tranny do the work by itself and don't shift unless in adverse weather conditions.

i have a 96 with 4.0 3 in body lift auto that hesitates shifting from 2nd to 3 rd i have to let off the gas so it will shift why

a number of issues. Tcc regulator bore worn out, the infamous check ball seat it hammered badly, or/and calibration issues. I have seen all three issues on the same trans - often!

i got a 1996 chev. blazer s-s10 4.3 engine 4x4.problem i got is i got 1st 2nd & overdrive & reverse but no 3rd gear what should i do

The possiblities that come to mind are
1 Bad synchro in transmission 2 bad bearing(s) in transmission input shaft.   3 Bent shift linkage or shift fork (I doubt this, but it's possible)
Only number 3 is relatively cheap.  I'd go back to where/who you bought the car from, if it was that way when you bought it, and ask them to help.  It can't hurt.

Using force is NOT the solution.  If the syncros are bad, until you get them replaced, you'll be better off to determine the RPM difference between 2&3 gears (maybe 800-1000?) and also 4&5 gears (maybe 500-800?) and learn to put a modest amount of effort at exactly the time the rpms fall into that diffference.  
Example Say the difference between 2nd gear at 3500 RPM and 3rd gear is 1000 RPM, then when you take it out of 2nd for an upshift to third,  delay until the RPMs are just getting to 2500. If you are on a budget and can't fix the transmission (it's going to be big bucks) you may find you can get pretty good at this.    It is possibly to shift a car this way without even using the clutch, although I don't recommend this and it takes a great deal of practice and luck.
While you have this problem, don't downshift into 3rd,  just run the RPMs down in 4th (say to 2000 or less) until you can shift into 2nd at an acceptable RPM. The least amount of shifting you can do until you resolve this the better.
Another choice until you can fix it, is to just run up the RPMs in 2nd and then shift to 4th, and then forget you have a fifth gear.  This is much better than forcing, it's possible to do more damage by forcing. 
Is it hard to get into 3rd from 4th AND 2nd?  
..ajm

I would first change the transmission fluid since it may be burnt. If this does not work you need to have the transmission checked out.