I am studying the HSK Level 2 list and have noticed that certain words only come up "reading" by typing in the pin yin and I don't get to practice writing them. Others only display in the writing mode and never ask for the reading. Is there a way to get a more random mix?

It's likely that the other parts which aren't showing up are being spaced out by the parts you are seeing, until you get them right more often. The reason it does this is because if you get prompted to write 例子, get it wrong, and then two minutes later get asked for the pinyin of 例子, then you'll probably remember it from just having seen it, not because you know it from the last time you were prompted for 例子's pinyin. So the system pushes the pinyin prompt back a bit until the writing prompt isn't getting in the way.

Does that make sense? If you think it's not just this intended spacing effect, you can let me know a couple words that you think aren't being scheduled correctly and I'll take a look.