I live in an apartment block that is about 100ft high. Every now and again, we get aircraft that fly over head without much clearance. For example, just now according to Flight Radar, a private plane flew overhead at a calibrated altitude of 550ft https://www.flightradar24.com/data/aircraft/ei-jia#29ecb897. I had another case where another private plane flew overhead at 350ft, sent details to the IAA with reg number etc., but they didn't seem to care.
What is the minimum altitude planes can fly at over built up areas in Ireland?
I believe the altitude displayed by FR24 is based on standard altimeter setting of 1013 hPa. The actual QNH at lunchtime today was about 1023 hPa so the FR24 portrayal of altitude is unlikely to be accurate.
By the looks of it he had to hold and subsequently go around and make a second approach so the intention was likely to land and not just low flying for its own sake.
If ATC instructs you to fly low then you must comply, unless it is unsafe for the flight. In general, though, the minimum height for flying over a built-up area is 1500 ft above ground level (agl), except when on approach to land, which is what that aircraft was doing (landing at Weston). The displayed altitude of 550 ft at a QNH (sea-level pressure) of 1023 hPa means a true altitude of 550 + ((1023-1013)x27) = 820 ft above mean sea level (amsl), which also happens to be above ground level along the Liffey.
When departing Weston and transitioning across the city to say Killiney, Dublin Tower usually instruct an altitude of no lower than 1700 ft asl, which guarantees 1500 ft above the ground.
If a plane was indicating 350 ft with a QNH of say 1040 hPa, its true altitude would be around 1080 ft amsl (add around +27 ft for every hPa that the QNH is above standard 1013 hPa. Conversely, if flying in low pressure (e.g. 980 hPa), then the true altitude would be -540 ft (i.e. below the ground). Obviously that's why you need to heed the saying "Flying from high to low, watch out below".