Door open on a PA38 nothing whats so ever apart from increased wind noise.
In fact sometimes the top latch is left open during summer just to keep the temp down.
If the bottom latch pops open which is actually quite hard to do it no great shakes only thing you need to watch is that if you stand on the brakes it doesn't go swinging forward and damage the hinges. Obviously if you start stalling or spinning you might get issues.