The author of Get Medieval does this to an extraordinary extent with medieval history. During one of the interludes she even draws a picture of Sir Gerard in the actual formal wear he'd have during that period (complete with pointy-toed boots), then explains that she put him in more "conventional" medieval attire because if she drew him like that nobody would buy it.
Schlock Mercenary has in various occasions shown their work. Military tactics, futuristic concepts and even current space theories find their way into the comedic space opera. Not only that, but it also introduces some tactics (like the Very Dangerous Array) that would actually be very effective in real world (if we ever reach that level of technology).
Most notably, in one of his earlier arcs dealing with the Lunar States, he described the number of levels on a space elevator and the movement rates of the elevator itself and challenged readers to calculate the height of the structure. It worked.
Dylan Meconis, author of Family Man, does so much research for her comic that there's a page of notes accompanying the pages to prove it.
The Dreamer was pretty much started as a healthy outlet for the author's obsession with Revolutionary America.
Brat-Halla is actually quite well-researched... and goes out of its way to show it when it's not diverting from mythology because it would be funnier. This comic is a particularly extreme example, quoting verse 56 and part of Verse 55 of Völuspá in the Poetic Edda, seemingly just to show that they bothered to research Thor's death, and render it as accurately as the storyline it happens in allows.
Unlike many fangirls, when Gina Biggs began creating a webcomic set in Japan (Red String), it actually resembles modern-day Japan and not fangirl-fantasy Japan, showing very clearly that she took the time to know what she was doing.
Irregular Webcomic! is chock full of obscure scientific, literary, mythological or otherwise obscure knowledge that makes the puns work. Arguably it's more fun to read the annotations than to read the comic.
Lackadaisy Cats features authentic 1920s slang, fashion and technology. Also, Zoot Suits, but most of it's good.
The only noticeable historical inaccuracies are the aforementioned zoot suits and one cathedral-style tabletop radio. Both are acknowledged by the author, who mentioned that she might changed the radio to something more accurate before that page is published.
The author bases all the buildings in the comic off of buildings in her home town of St. Louis, which is also the setting of the comic. She also references lyrics from popular songs of the 1920s. She dates many things in the comic, such as characters' dates of birth, letters, and photographs, with painstaking detail.
Clint Hollingsworth knows tracking, and uses this knowledge as part of the premise for The Wandering Ones.
Terinu author Peta Hewitt is a practicing nurse, so any medical details in a hospital scene are either accurate or logical extrapolations. Not to mention she used to work in a children's ward, so her depiction of her eponymous troubled teen hero's psychology is well grounded also.
Kilgannon does this with A Miracle of Science. Discounting things that are obviously visual aides for the audience (like eye colour change when being possessed by Mars (though that's Sachs' fault)), the background work is obvious and he can't resist the temptation to rant about science a little bit (significantly more science ranting and explanation happens in the comments with each panel).
Hastings and Archer, creators of The Adventures of Dr. McNinja are very studious and take great care to research what the characters are dealing with. Everything from blood transfusions to submarine classes to in what part of the country you can find MTO setups. As if we need another reason to go gaga over this comic.
Two words: blood loss. The eponymous doctor backs out of a fight due to blood loss.
This is in the same part where Dr. McNinja's "doctor half" argues with Death over whether or not his injuries were actually fatal (although it's really just a ploy to allow his "ninja half" to sneak up behind Death).
In Wapsi Square, when Paul Taylor decided to introduce a mysterious artifact on a sunken U-Boat, he actually made sure to choose a specific one for which the known details of its disappearance don't contradict the events of its disappearance in the comic. He also researched a bit of information about the interior of such subs and German WWII grenades.
Gunnerkrigg Court have more fine details than pages with "113" written somewhere, and does it right — all the time. To the point where fans regularly feel compelled to also do the research after the current page. Yes, this became another layer of entertainment in itself.
One chapter spends a few pages talking about historical fencing — in particular, the style of Johannes Liechtenauer, German knight and swordmaster of the 14th century. The source material for such a reference is so obscure that many modern studies of warfare in the period fail to take it into account.
The author of the Hark! A Vagrant strips, Kate Beaton, has a degree in history and anthropology, and it shows, what with strips centring around Antonio José de Sucre, Mary Sidney, Georges Cuvier and others that may be completely obscure to most people.
The author of Era Of Errors has spent most of his life researching and learning about various fields of science and health due to numerous problems during his childhood with his own health. These elements of real-world, cutting-edge science will be frequently woven into the story, with slight exaggerations here and there for aesthetic/advancement of the storyline reasons.