There are many different ways to make HST's. How are you doing it? Are you first cutting triangles and then sewing the triangles together? Or are you cutting squares first, sewing twice down the center, and then cutting? Or.....?
If you are doing either of the two above methods, I would advise starching the fabric as heavily as possible before cutting the triangles or squares. This stabilizes the fabric so it is much less likely to stretch or distort while you are sewing and pressing.
Cutting over-sized and then trimming down is very accurate, but it does add some time to the process. If I were using this method for making lots of HST's, I would invest in the appropriate size Bloc Loc ruler:
http://blocloc.com/
My current favorite method for making HST's is to cut triangles using the Accuquilt Go! The Go cuts very accurately and lops off the "dog ears", making matching up the ends very easy. I do not pre-wash my fabric so I don't have to starch, as there is enough sizing in the fabric already to keep the triangles stable once they are cut.
I also like using Thangles to make HST's. This method is very accurate, but you do have the extra step of removing the paper. These are widely available, but here is a link to their home page:
http://www.thangles.com/howtheywork.html
My best guess about your problem is that, even though you are taking care when cutting, the triangles are getting distorted when being handled and sewn. Remember, you are sewing bias edges together, and bias edges are very prone to stretching.