Transmission

The transmission should shift, as you say it should. It might be a ball valve in the valve plate that has some air in that part of the system which is preventing the third gear from engaging, or, there is a band adjustment that simply has not shown up until now. I think a trip to a transmission repair shop for their evaluation might be a good idea. One other point that you didn't mention, and should have been part of the check, the filter should have been changed. You also need to check the operation of the modulator valve. The transmission shifts by virtue of engine vacuum. If that part of the system, or any linkage is not right, then there will be shifting problems. These can be checked by yourself, if you know what you are looking for, or, as I said, go to a tranny shop. If you do, be sure to tell them all that you did, and that you did not replace the transmission filter. That filter is in the bottom of the transmission, and is accessible by removing the bottom pan of the transmission. source

I think it adds additional information to state if you have AWD or FWD. It seems in the 1st generation RX's the AWD versions had significantly more problems. My wife had a 2001 RX300 with FWD that we passed on to our daughter that now has 114,000 miles on it with, I'm not proud to say, nothing ever being done to it in the way of transmission service. source

Apple will probably disable, I'm sure they could have added FM to ipods years ago, but to this age we still don't have them. Anyone believing they will add them to the iphone must not know Apple or must be living in la la land. source

I think they are technically called transmission "isolators". They are the skating wheel type bushings that hold up the tail end of the tranny on the cross member. source

I keep hearing nothing but good things about him. JasonTDI, up in Wisconsin, highly recommended him also. I just wish I wasn't going in for a repair, it would have been nice to get the LSD that he is offering. source