I'm refitting a boat and there's a lot of plywood to cut in odd shapes. I'm damned if I can cut the stuff straight with my jigsaw -- had to cut out a rectangular cupboard door opening in a sheet of 9mm and it looked like a drunk had done it! Have I got a cr*p jigsaw (old Bosch) or do I need glasses? (I can saw nice and straight with a pull saw BTW)
That does help on long cuts but tricky in small areas or cut-outs like drawer openings. Could I router the cut straight or would that tear up the edge of the ply?
The problem is likely to be the blades you are using. A poor kerf will drive the cut off line. If the blades came with the saw just throw them away. Otherwise replace your old ones with reasonable quality ones. Screwfix will sell you them. The next likely cause is the blade holder on your saw. Make sure the blade is seating properly and the mechanism is tight. The third likely cause is ...erm you. Relax, don't push the jigsaw along, watch the blade follow the line and wear safety glasses.
cheap jigsaw + cheap blades = wonky cuts. Get a decent jigsaw ( Bosch pro, Makita or Metabo ) and buy good blades designed for the material you are cutting - and practice makes perfect too.
I would have to agree with HOTDOG and ceq999. You are only as sharp as you're bluntest point and cheap/old blades will make even the best saws perform well under par. I have a Bosch GST 135 BCE and it gives great performance.
Replace the blade first - there are many available from screwfix and will tell you which is suitable for your thickness of ply. If the blade doesn't make any difference then get a new jigsaw as recomended above. If the blade and the jigsaw don't make any difference then maybe you need to clamp or screw some battens as guides to give a good cut. It's not easy getting a perfectly straight line with a jigsaw but your problem seems to stem from pushing the jigsaw whereas you should be more guiding it if you have a good blade and saw.
If you have a good eye and a steady hand then blades are the thing to look at, cheap ones tend to overheat and warp, (pushing too hard on the jigsaw makes the problem worse) use a good quality blade, Bosch are very good, but if you are prepared to spend a bit more buy Festool blades, they are a thicker blade and will stay perfectly straight, the rest is down to the eye and hand.
the basic problem here is that you have not understood what a jigsaw does it is designed with a narrow blade so it can cut a curved line. it is not designed to cut in a straight line it is however also correct that good quality jigsaws and blades improve your abilty to cut a straight line