We have just installed two 2-piece toilets. We have an intermittent but regular problem with flushing the toilet where upon flushing you hear/see an airbubble and then the toilets fills with water but the swirling action is only half hearted and the toilet doesn't drain away. A second or third flush will result in a normal flushing action.
It may also be that the water level in the bowl may seem low at the time of flushing if this problem is about to occur.
The water flow sound at the time of the flush also sounds "half hearted" compared to the "whoosh" when the toilet flushes normally.

If these are new toilets then look to the installation folr the problem. I have found that when the installer installs a new toilet they don't "bevel out" the wax seal. Unless the seal is slanted towards the outside of the flange it will spread inwards. This closes up the hole around the horn to the point that when you flush it will set up a back pressure causing the syphon action to stop. You'll have to flush a couple of times to get it to flush right. I ran the service department for a large company. I begain to get callbacks from our new constructions that the toilets weren't flushing properly. I wentout in the field and pulled a few. All had the wax ring spread out covering the closet flange and choking down the flush by backpressure. I had to set up a service clinic to show our plumbers what the problem was and how to correct it.
When they begain to bevel the wax rings outwatd the complaints stopped. Go back and pull the toilets. If you find the wax overlaping into the drainage area then trim and bevel it so that it will spread outward instead of on to block the flush. Good luck, tom

That doesn't seem to have fixed it, I am still a little suspicious of a largeish bubble of air coming out of the jets when you initially flush?

That doesn't seem to have fixed it, I am still a little suspicious of a largeish bubble of air coming out of the jets when you initially flush?
I can take the mystery out of it but I can't suggest a repair. When you flush the water from the tank goes into the top of the bowl and the rings before exiting out the jet and rings. The cavity in the top of the bowl then fills with water pushing the air ahead of it. This air is what you see. If both toilets do this it may be in the design. Check the water level. It should be 1/2" below the top of the white over flow tube. Now check tosee if the small 1/8th" plastic tube is connected to the ball cock and is going into the white overflow tube this tube fills the bowl while the tank's filling. I had hoped it was the installation of the wax rings that gave you the problem but since you state that you pulled the toilets and checked I'm running out of answers. Regards, Tom