There are a few features that will cause unpleasant things to occur with g(Math). One that is frequently encountered is when a long expression is entered into the Enter LaTeX box. When the expression is too long the LaTeX Preview image can scroll off the right of the Sidebar. You can manually scroll over to see the entire image.
If your expression is too long, it will not render and give the broken image icon. It will also not render if you try to Insert it into the Doc or Sheet. This is due to a restriction with the Google Image Charts API. Unfortunately, the exact length that is allowed is not disclosed. You can split your expression into two (or more) images and put them side by side to create the same effect as 1 complete image expression as a workaround.
There have been a few instances of the image not inserting correctly in the document. Sometimes clicking Insert again will remedy this or refreshing the page and trying to Insert again. If you are having other issues, please click on the Help->Report an Issue. If you leave your email address I try to respond within 24 hours with a fix (if it exists).