Passenger side only blowing cold air.

There should be ( 2 ) slide switches or buttons that control passenger/driver side climate control, one of the switches is not operating correctly and probably be faulty. I have a 1991 Buick Regal with the same problem, sometimes i can slide the faulty one real fast to the right and back to the left and it will work fine.

Same problem on my 98 Regal GS; remove glove box, locate the blend door actuator, (black odd shaped box with metal "ring"). Remove the box and manually turn the blend door shaft it was attached to. If you get cold air, it's the actuator you removed. About 30-40 dollars.

you need to replace the actuator most likely

THIS IS A GUESS. Both sides probabley have "mix" dampers that regulate temp by mixing hot and cold air to make you comfortable. Passenger side must not work properly, stepper motor? Dirty actuator? Temp sensor on passenger not working? Don't honestly know but I'm not sure a do it yourselfer could figure it out. Sounds complicated.

the motor for the passenger side
blend door is shot

Your passenger side blend air door actuator has most likely failed. I hope this helps.
Thank You,
Roy

Vent door between the two sides isn't opening or the flex hose going between the two is off.

problem with blend door either stuck or linkage problem

I had the same problem when i was working on my 1999 Buick Regal and had to disconnect the battery. I didn't reconnect in the same way that I disconnected the battery from the terminal and noticed that the driver side had no heat or air but the passenger side did. I then disconnected the battery again and reconnected it the same way and now have heat and air on both the driver and passenger side. Hope this helps. Good Luck!

Most likely the blend door motor is defective.