I had this same problem with some warm air only from passenger side and cool air from driver side. Problem was fixed by flushing the heater core several times in each direction with water from the garden hose.
Now have hot air blowing from both sides. No chemicals were used.

 

Well 6 weeks later winter is getting colder and I don't have enough heat . Not sure whether I am getting less heat since the original flush or it is just colder. Heat at this time is about equal from both passenger and driver side vents.
So I reflush (compressed air and running water through it with a garden hose) again and this time it definitely seemed to be partially blocked. Also use CLR leaving it in the core for 30 minutes. See what happens now.

 

Is there any way to get an actual picture of what this looks like on the car? My bf just paid $650 to have new radiator put in (it had cracked) and he had previously put stop leak in it. After he put the stop leak in the car the heater issue started. The mechanic supposedly flushed the heater core but he still has this issue. I told him that I think that maybe the stop leak plugged up the heater core and that they probably didn't back flush the heater core when they worked on the car. If we do the backflush and it still does not work is there anything else that could be the problem? We checked the heater control ***** all is perfect there.

 

i dont think i have a picture but theres two hoses connected to pipes coming out of the pass. side firewall its under the washer fluid tank which comes off with two 10mm nuts. the hose clamps are the spring loaded kind. ill see if i have a pic