Election result announcers are being urged to put in a more consistent performance, with some being dubbed "inaudible".
The Electoral Commission found returning officers' overall provision of information was "patchy", while there were "significant variations" in the time taken to count votes.
But it added that more than 90% of people were happy with the handling of English local elections in May.
More than 5.6 million people voted.
The elections on 2 May took place across 27 county councils and eight unitary authorities.
There were also elections for Anglesey County Council and a parliamentary by-election in South Shields, prompted by the resignation as an MP of former Foreign Secretary David Miliband.
The Electoral Commission's survey found that 88% of people were satisfied with the process for registering to vote, while 97% of those who voted at polling stations and 96% of those who cast postal ballots were satisfied with the service provided.
Some 140 "potential cases of alleged electoral fraud" were reported, although the Electoral Commission found no "major problems" with administration.
But the South Shields by-election, which was announced only the minimum 13 working days before it was held, had "placed pressures on the administrative process", contributing to a "significant shortening of the nomination period for candidates".
Around England, returning officers' "provision of information in count centres was patchy, with some... making better use of announcements than others to keep everyone informed as the event progressed".
"In some cases announcements were infrequent, or inaudible," it said.
And the commission found that "in some cases the layout at some counts made it difficult for observers, candidates and agents to see the ballot papers as they were counted".
And there were "significant variations" in the times taken to tally votes.
Electoral Commission chairman Jenny Watson said: "We've set out in our report where we think there is more that can be done, and I encourage all returning officers and their staff to look for opportunities to deliver an even better service for voters and candidates at future elections."
She added: "These elections were well run and elections staff should be congratulated for this achievement. But the challenge of maintaining and building on this success should not be underestimated."
The commission's survey, conducted by BMG Research, took place from 3 to 19 May and involved a representative sample of 1,003 adults.