I've found it incredibly glitchy. I have some reminders that somehow duplicate and show up multiple times (all at the same time), and others that will show up and instantly dismiss themselves. I can even be looking at my phone and see them pop up and instantly disappear.
For a long time I thought it was perhaps due to poor sync with the Mac, since sometimes I manage reminders from there, but the same thing happens with the wife's phone and she doesn't sync Reminders. She has a single daily reminder at 10pm. Sometimes it shows up 4 times. Sometimes 4 times and 1 disappears for a net of 3 reminders. Sometimes just 1 shows up. Sometimes none of them show up. It's bizarre.