In addition to making sure your rulers are still square and your cutting surface is not bowed (note: A folding card table is never a good cutting surface but I've seen them used often), consider ergonomics.
I find I cut long (width of fabric) cuts best standing up at my dining room table, smaller and trims I can do fine sitting, but I have a long torso and relatively short arms and skew long cuts while sitting. A taller friend of mine found standing at her kitchen counters made a huge improvement in her cutting accuracy.
And one more mention about straight of grain. It's one of the reasons I believe in pre-washing and typically I rip off one side before washing so I know where the straight is. Cuts are often off grain by up to two inches. Some of it is because of the way the fabric is made, and then wound on the bolt, some of it is the cutting. Back in the day of home ec classes, we were taught how to pick out a thread for the straight edge, trim along that line and then tug on diagonal corners to straighten. I was taught that straight of grain was important and sometimes it is...
On the other hand, with modern woven fabrics straight isn't such a big deal for the most part. I happily fussy cut fabric all the time with no attention to the grain at all. Some people believe being slightly off grain is beneficial, yes it is true that my squares are so square they are right on grain, but if your fabric is so flimsy you need to worry about threads shedding then you shouldn't be using them.
With smaller pieces (yard and under, including fat quarters) I wash them in my normal wash (warm) with like colors and unscented soap. I've dye checked anything I'm concerned about, but usually not an issue with commercial fabrics. I want them to be roughed up a bit and come in contact with the other pieces. When they come out, I give them a good "snap" (you will know it when you hear it!), and toss them in the dryer. I don't use dryer sheets with my fabric and I'm pleased with the woolen dryer balls I've been using. I also wash the larger pieces but they don't snap
