Is there a problem with flies and mosquitos in Salter Point?

Mosquitos yes. I have been renting here for about 6 months and once it hits night time expect to get bitten if outside. Not sure of flies have not been here in the heat. The mossies are pretty frequent around the river and parks though everything else about this suburb outweighs the small problem of bugs. I'm sure with some bug repellent the problem would be minimised and this area is so lovely, such close proximity to the city and freeway, the people in this suburb (including the kids even) are polite and friendly always happy to have a chat at the park with the dogs.

By the river, you are likely to have some mosquito problems. It is more problematic where the river doesn't run as efficiently - eg near the lagoon. The City of South Perth does generally have a mosquito management program in place. I've come by the following management report from 2017-2018 which will hopefully help.
https://southperth.wa.gov.au/docs/default-source/1-residents/services/mosquitoes/city-of-south-perth-mosquito-management-plan2017-2018.pdf?sfvrsn=b718ffbd_6

Yes to mosquitos near water area's and Salter Point is a Riverside suburb. Mostly prominent at sunset / sunrise and evenings.