I have a 2003 F350 Crew cab DRW 6.0L Diesel. I have been experiencing problems with the trans all summer. It seems the tow/haul light starts flashing and at that point the trans starts shifting irregularly. Such as starting off from a dead stop, the trans will be in 2nd gear or at higher highway speeds it doesn't down shift as it should when calling for more acceration... All of this only gets worse if I tow my boat. So far we have changed out the shift solinoids with still no luck..
I had a similar problem with mine in the spring, my fix was the TFT sensor in the trans was bad. It would run fine for a mile or 2 then the trans temp gauge on the dash would bury hot and I would start getting the weird shifts. If this is your problem, it's a very easy fix.
Now, this is not good. Even though these codes could be related to a faulty shifting solenoid, but a solenoid usually have it's "own" DTC.
I've had symptoms as you have, and I've had gear ratio and friction element codes, and I ended up rebuilding my tranny......
What do you mean it shifts irregularly? Is it slipping?
I understand that it gets stuck in 3rd gear at a stop. Do you have any symptoms in reverse? I'm asking, because the week part of the 5r110 transmission is the direct clutch, and if you have a problem with that, it will get stuck in 3rd gear sometimes, you also will notice slipping between 3-5th gear, but it also will act weird in reverse ( delayed engage, shaking ).
Anyways, the bottom line is, you got friction DTC-s, and you mentioned that you drove the truck like that all summer long - and towing a boat, so I believe that you will facing a tranny rebuild. If you like the challenge, you could do it yourself, but I'll tell you by experience, that it's one of the hardest jobs on the 6.0 - mostly because dropping and reinstalling that heavy beast. But it's still doable, and if you decide not paying about $2500-3500 on labor I highly recommend getting a torqueshift rebuild manual - you can find'em on ebay.
For the time being you could try replacing the fluid, but i doubt that will help.