After the critically acclaimed first episode aired on January 5 this year, some baffled viewers accused the actor of "mumbling" - to such an extent that they were struggling to understand parts of the plot.
ITV said at the time that it had received "fewer than five" complaints about mumbled dialogue.
One of the Twitter users suggesting that this may be the result of a stronger Scottish accent was Anuja P, who wrote: "Has Tennant gotten more Scottish in the new series of Broadchurch?"
But Walaa Mancy was just content to see the actor on screen, tweeting: "I find it a little bit difficult to understand the Scottish accent, but it's David Tennant, so who cares?"
An ITV spokesman this pointed out that David Tennant was Scottish and merely speaking in his own accent "as he usually would in every day life". He denied that it had changed in any way.
It is not the first time Broadchurch has sparked debate on social media.
Some have complained about this season's plot line, claiming there are a number of inaccuracies in the way legal proceedings have been portrayed
Elsewhere, mother Beth Latimer, played by Jodie Whittaker, prompted ridicule when she returned to court to witness the trial of Joe Miller a short time after an easy water birth.
Comment from Tennant's representatives has been sought.
- Daily Mail