A CA glue is cyanoacrylate one like Superglue. It is offered as a gel or very thin one. Also for attaching a such "glassy" thing you can use the Humbrol Clearfix for instance. But it seems that your problem is not with a glue but with the way you stuck these cockpy conopies. There is no need to apply a glue at all edges of a fuslage or a conopy. Usually it is enough to put a small drop of a glue at two or three places.
OK, that's exactly my mistake. One would think that a reasonably intelligent modeler would figure that out in time. Guess you know what that makes me, eh?
Wild guess here: I'd say you've glued the clear parts in place after you've painted them? In addition to a somewhat ragged looking join that's not easy to touch up without wrecking the surrounding paintjob the paint coat also is wrecked by the use of (regular) glue, which doesn't help matters as far as the overall result goes. Use of other types of glue should prevent this. In addition toying with the order of masking, painting and installing the clearpart could help.
For example, I tend to mask my clearparts while they're not installed.
You were right, it was a wild guess, and incorrect, though not an unreasonable assumption. In fact, I also apply the masking to the clear parts before I attach them to the model. I also attach the clear parts to the model before I paint, but I'm just not good at it, evidently.
I don't like the idea of a white glue since they do not cure completely clear. as other have said there is little stress on the canopy so I have taken to using Future to "glue" the canopy in place. Again, just a small amount and put the canopy in place while the future is wet. in 30min or so the future will set and the canopy will be in place.
As far as CA glues are concerned I have had problems with the fumes clouding up the clear canopy even through the Future coat
Future? I never thought of using it as a glue before. I use it on models, and other plastic parts as a sealer. I'll have to try that out.
So CA is Super Glue. I hate that stuff. I seem to always end up with some on my fingers, and I'm with Mikewint in experiencing clouding on the clear parts, usually due to lack of ventilation inside the cockpit.
Elmers sounds just about right to me. It doesn't go by that name here in The Netherlands, but other US modelers keep calling it Elmers, so I'd say yes Elmers is what you should get.
Sorry, I keep forgetting that there are plenty of other Nationalities on this forum than U.S.A. members. I know, another arrogant North American. I don't mean to be, though. Honest.
To sum this up, I have been using way too much model glue on the clear parts, and I shouldn't be using model glue on them at all. I need White glue (Elmer's

). or maybe even Future, and only a tiny dab in two or three key positions around the edge of the cockpit. Lastly, I'm an arrogant American with no common modeling sense.
Have any of you used the Testors Clear Plastic Glue? I use it every now and then, but I guess it must not be much of a choice.