As bearisgray wrote, you want to focus on what size your units are ending up. There are two possible causes of problems: cutting that is slightly off, or seams that are slightly off. (A person can have problems with one or both.) I suspect a lot of starting quilters have problems with being slightly off in their cutting, and one piece of evidence that supports my theory is that many people who switch to cutting out their pieces with dies (such as by the Go! Fabric Cutter) report that their piecing becomes more accurate. It is very important to get the measuring line of your ruler *all* the way onto the fabric, not next to the edge or part way on.
bearisgray wrote a good test to do with sewing four strips together. I highly recommend doing that test and then pay particular attention to the width of inner two strips. Each of them should be exactly two inches wide, the whole length of the strip. If they are not, either your cutting or seam width needs adjusting. If you've *thoroughly* checked, your cutting results, then you can work on fine tuning your seam width.
For avoiding problems with the tendency of many machines to want to swerve at the end of seams, I have found using a walking foot to be very helpful.