Nintendo said such pixels were "normal and should not be considered a defect".
But one analyst said if the issues were as bad as online photos suggested, it was "unbelievable" Nintendo had let them leave the factory.
The Â£280 handheld console went on sale on Friday.
Sales figures suggest it has become the fastest-selling games console in the Japanese company's history, with reports some shops have already sold out.
In the UK, it has sold an estimated 80,000 units.
The Switch can be played both on televisions and as a standalone device.
It launched with a handful of games, with some critics saying there were too few.
And now, thousands of customers have reported their new devices came with a screen problem.
On a Reddit discussion thread, one user said: "I understand they're apparently common in devices, but in a handheld system it's a big enough annoyance for me I would not purchase a device with one."
He said he had a similar problem with his Sony Playstation Portable.
"My first one had dead pixels in the middle of the screen, and I brought it back to the store I purchased it in," he said.
"Luckily, it was a big news story so they were allowing you to open up new boxes in the stores and turn on the device.
"I went through three and on the fourth got one without any visible dead pixels."
Nintendo responded on its support page, saying: "Small numbers of stuck or dead pixels are a characteristic of LCD screens."
A similar pixel issue also affected Nintendo's DS, and the Japanese gaming company eventually allowed buyers to replace devices.
Paul Gray, an analyst at research company IHS, said such issues should no longer be common.
"In the early days of LCD screens there were lots of defects, but these days you see fewer and fewer of them," he said.
"Some of the photos I've seen posted online, I cannot believe that Nintendo would have knowingly let them leave the factory like that.
"Something doesn't ring quite true," he said, suggesting that some of the photos may have been doctored.
Mr Gray advised anyone with a defective device to return it to the shop they bought it from.
"If you are a consumer and you find it irritating, you should go back to the retailer and say that you are not happy," he said.

The former Nottingham Forest defender signed for struggling Longford AFC in January in a bid to end its season-long losing streak and 178-goal deficit.
He was due to get his boots on for the Gloucestershire non-leaguers last month, but the match was called off.
A club spokesman said with Pearce on side, it was hoping to get its "very first win of the season" on Saturday.
Rooted to the bottom of the Gloucestershire Northern Senior League Division Two, Longford AFC has lost all its games this season and conceded nearly 200 goals - earning it the name of "the worst team in England".
But following their star January signing, club treasurer Mike Dean said the squad had been training hard and "games haven't been as bad".
"We went down to Bisham Abbey - the old England stomping ground - a couple of weeks ago with Stuart and were training down there for about two-and-a-half hours," he said.
"We have been getting beat but the scores are only 1-0, 2-0 - very low now.  So things are getting better and the confidence is in the side."
On Saturday, 53-year-old Pearce - nicknamed Psycho - will be turning out for Langford AFC in a bottom of the league clash with Wotton Rovers.
Simon Graham, Wotton Rovers manager, said it was "chuffed" but their right winger was a "little bit nervous" about marking an "ex-England superstar".
"We've got a young squad and Stuart Pearce's legs aren't as fresh as they used to be so we'll run some rings around him," he said.
Pearce, who won 78 England caps, was part of Sir Bobby Robson's squad that reached the last four of the World Cup in Italy in 1990, and the Terry Venables-led side that was eliminated at the same stage of Euro '96.
He retired from playing six years after that, having enjoyed spells at Newcastle United, Manchester City, West Ham, Coventry and non-league Wealdstone, as well as captaining Forest under the management of Brian Clough.
Thousands of owners of Nintendo's new console, Switch, have complained about dead or stuck pixels creating distracting and annoying dark squares on their screens.
[NEXT_CONCEPT]
England football legend Stuart Pearce is set to finally make his debut for a team dubbed "the worst in the UK".