I bottled about a month and a half ago. Every bottle I tried has had no carbonation. But I just opened up a bottle and it was over carbonated, and it almost exploded out of the bottle. I had this problem with another batch last year. Almost all the bottles had no carbonation but I had a few bottle bombs. Could it be that the priming sugar didn't mix enough in the bottling bucket and it all just went into a few bottles?
It does sound like your priming sugar wasn't mixed very well. That said, if the flat bottles are sweet to the taste there's something else afoot.
When I bottle I usually mix a cup of water with 3/4 cup of corn sugar and stick it in the microwave for a couple minutes to boil it. I then let it cool for a while before pouring the solution into the bottom of the bottling bucket before racking the beer. After that, I gently stir the sugar into the beer with the auto-syphon before filling any bottles.