I'll 3rd what Beckibee said for appts.
I had 2 ultrasounds the first at around 10 weeks. The second was 18 wks for #1 and 23 wks for #2. The delay for #2 was due to christmas it was hard to get appt.
The ob also had his own u/s machine and toward the end he'd check the fluid levels every week when I went there for appt.

I don't think they reccomend any further scans unless they find something they want to keep an eye on.