While some warnings were being issued relating to possible breaches of the level 3 restrictions on movement, he said "by far the majority" of people were complying with instructions, including that they should return to their homes if not on the road for a legitimate reason.
Some of the checkpoints were more prominent than others, including state highway checks, which had "turned back" travellers entering Hawke's Bay from further afield.
Among those turned around were tradespeople, who in the circumstances were not permitted to work outside their own areas.
"We are taking note of feedback on people's reasons for being out and about," Broderick said. "But we've got to be aware moving around is still just for essential or permitted purposes."
Some people could find they may still be restricted on the road when alert levels are lowered, after being caught for speeding during the lockdowns.
Broderick said some people were taking advantage of fewer cars on the highways, and at least two had been suspended from driving for 28 days for breaking the 100kmh limit by more than 40kmh.