Hi,
We have stayed in Figuretes twice now and both times had a great time with no problems at all to report. The staff at both the Lido and Rialto (now private appartments) were excellent and very helpful, especially when the ceiling fan broke in the Rialto on our last week and they fixed it within an hour of reporting it was faulty.
I guess its some of the horror stories that we read about in the press that tend to put the wind up us, as I was told twice before we went to Figuretes that it was a red light district and there were a lot of problems with street walkers and drugs, and that there were a lot of gay men having sex in public, none of which I am happy to report we encountered.
Some of the rumours tend to come from the fact that there is a strip bar in the town, but you shouldnt have to much of a problem, even with smaller children.
As for broken glass! The main area to avoid is up at the far end of the beach of Figuretes, just down from were all the restaurants are on the promanade. There is a rock jetty that juts out into the sea and this tends to have a great deal of broken glass lying around on both the jetty and in the water near it, so please be careful.
Other than that the beach is one of the nicest on the island, very clean and swept every day during peak season, and it is very shallow so is ideal for smaller kids and toddlers.
Hope this helps, if you need any more advice please let me know or check out my website as I have reviews of the area there.
Marc