I'm curious what enlarger you are using where the neg-carrier is plastic?!
The neg usually curves slightly in a plain carrier, so that the middle of the negative is higher than the edges (which are held in the carrier). The top glass should be able to stop the bulge and keep the negative flat, though a double-glass carrier is better still for flatness and becomes significantly more important with larger formats. When the neg is not flat you will have some difficulty focussing both the middle and the corners at the same time plus the amount of curve of the negative may even change during the exposure -- definitely not helpful.
One occasionally seen problem is the appearance of Newtons Rings between the negative and the glass surface. These can be eliminated by one surface having a very, very, very slightly rough surface -- hence "anti Newton-ring" (ANR) glass in negative carriers. It appears to be slightly grey looking but this does not affect the image, as the glass is above the film. If you use a lower glass too, as in a double-glass carrier, the tiny roughness of the emulsion is usually enough to prevent the ring effect.
If you can get to Photofusion hire-darkroom and training centre, in Brixton, they will be able to show you the differences in the various neg-carrier designs as well as giving all sorts of other advice to "hit the ground running" with your printing. Have fun!