I find it's easier to leave the pins in. That said, I DO NOT place pins in the seam area. I pin the blocks together about 3/4 of an inch from the edge of the block. I place the pins parallel to the edges of the blocks. I pin the blocks together on the seam line, and then I re-pin the extra distance from the edge and remove the first pin. It works for me. That keeps everything together, the pins are never under my presserfoot and I don't break needles on them.

I press my block after I finsh piecing, then square it. Then on to the next block. Sometimes I will sew the blocks in rows, other times in blocks of four. It all depends on the design. Also I press each row before adding the next row. It is much easier to press row by row, then the whole pieced top.

Lots of interesting suggestions.One not discussed is the thread size. Thread does take up space when the squares of segments in the square are pressed. If there are lots of patches in a square use a finer thread; the sections should be measured before moving on to the next step. As mentioned several times pinning carefully will keep the pieces from skewing as you move down the seam. Remember that the feed dogs always draw the bottom fabric a little bit-that little bit grows alot in a long seam if not carefully controlled. When I join long rows of blocks I use my walking foot rather than a regular foot-just like the process of adding long sashing and border strips. One more thought, when you mark your machine with tape for a consistent 1/4 inch seam be sure to elongate it behind the needle so that it feeds completely through the machine.

As someone who has made several hundred quilts, I agree with all the suggestions above and have several other things to add:

1) If you are pinning but still get bad results, the pins are too thick. I use the flower head pins, long and thin. My seams match exactly 99 percent of the time.

2) When piecing, I often use a quarter inch foot. If you don't have one, use a blind hem foot and set the wheel to a scant quarter inch, and tape the wheel down.

3) If I have any doubts about accuracy, I use a METAL measuring devise often found in fabric stores. I looked for a picture for you and didn't find it. However, it is a more or less square shaped irregular piece of metal about an inch or two square and has measurements for 1/4 inch, 3/8 inch, 5/8 inch, and more. This is a must-have notion for me.

3) I use leaders and enders to stabilize the pieces I want to be accurate (all of them)

4) I use a trolley needle, worn on my finger, as a stiletto. You could use a seam ripper to guide that last part of the fabric through.

I would try nesting, or butting the seams, and a pin in each side, walk the needle right up to the first pin, take it out, do the same with the second pin...