My city has also recently got them. Parking isn't so much of an issue (there aren't that many yet, and our sidewalks are quite big so there is a lot of space) it's just how people drive them. Mainly I'm just concerned how long it will be until someone is killed, and then the city will most likely outright ban them even though they are a good idea.
Most cyclists ride on the pavement as it's not really safe to ride on the road. They are lots of potholes and drivers aren't really aware how to share the road with cyclists. Maybe scooters can help change this, but anyway.
At pedestrian crossings, cyclists are required to dismount and walk their bike across. The majority of crossings don't explicitly stop traffic, but require traffic to yield to pedestrians. There are a lot of junctions with traffic lights where if you turn off the main route, as you turn you need to yield to pedestrians. If a bike is coming at 15km/h towards the crossing, your chances of seeing it are a lot less, hence the law. Scooter riders of course don't follow that rule, and at night with their dim lights (which may be coming from behind you, so in your blind spot) you aren't going to see them.
Once I was driving along a fast three lane road. The speed limit is 40km/h, but most people do 50-60. There were two scooters coming the wrong direction in one of the lanes - there was a perfectly useable sidewalk that they could have used.
Another time I pulled off from a red light, going straight across a junction. A scooter drove across the pedestrian crossing parallel in the same direction, then at the end swerved right in front of me, switching from the pavement to the road.
I think part of the issue is that you pay per minute. It causes people to rush and act irrationally, rather than taking their time and being safer. I've seen the same happen with car sharing schemes where you pay per minute.