I saw Day of the Dead (1985) for the first time a long time ago and tonight was the first time I’ve watched it since.
In the first 30 minutes, I picked up on three references:
1. 28 Days Later
Now, this is more of a minor coincidence, but when Miguel is yelling to see if anyone is alive in town, it’s not just that Jim does it in 28 Days Later, but Miguel even sounds like Jim (or vice versa I suppose). It was the sound of Miguel’s voice that was so familiar at first, not what he was actually doing. Hear it at 3:18
http://www.youtube.com/watch?v=VjWKlIEpPE4
2. The Cabinet of Dr. Caligari (1920)
I can’t imagine Romero making a horror film and indirectly costuming Dr. Logan like the infamous Dr. Caligari
Dr. Caligari
Dr. Logan "Frankenstein"
At the end of Caligari, we see the doctor sans top hat and looks a lot like Logan’s appearance. Definitely a nod.
3. The Big Lebowski’s Walter Sobchak (John Goodman)
This could be coincidence, or it could very well be direct influence, but Private Steel (Gary Howard Klar) immediately reminded me of Walter during a cafeteria scene in which he fits the exact visual profile of The Dude’s most boisterous bowling buddy:
Private Steel from Day of the Dead
Walter Sobchak from The Big Lebowski
Click to 9:03 for a better look at Steel:
http://www.youtube.com/watch?v=0FOR4TXyvJc
Day came out in 1985, well before Lebowski in 1998. Who knows….
Other Tidbits
Further, it was interesting to see a strong female character that reminded me of Ripley, yet came out a year before. Placed with Romero’s Night of the Living Dead (1968) and Dawn of the Dead (1978), it follows the same story and character structures: black man and white woman fight the dead and crazy, over-aggressive white guys (Night, Dawn, Day); in the latter third of the film, dump in a montage of zombies eating to really hammer your disturbing film home (Night, Dawn, Day).
Evidently the film did poorly because Romero wanted to do the project unrated for artistic purposes (rating the film would earn it an X/NC-17 and effectively rule out mainstream distribution; he preferred taking a chance that cinemas would accept his unrated film, still a big taboo for cinema owners). Due to the unrated path, his budget was cut and larger sequences were shelved until Land of the Dead (2005).
Overall not bad. Thinking zombies and the film’s somber tone made it interesting. The military guys keep hitting the same dull key, with the main bad guy, Captain Rhodes, maybe doing the worst. The Dr. Sarah Bowman character (Lori Cordille) is probably the best female lead of the whole Dead series (over time, Romero seemed to figure out how to write non-idiot females) and finally, the special effects are great, as it seems Savini was able to talk Romero out of using the same bright blood from Dawn.
The film genuinely scares, go see it*
*but make sure you don’t watch the horrible re-make done in 2008 that features Mena Suvari and Ving Rhames.
The Filmsmith 
Okay, so… For my money, the first two references you mention are almost certainly intentional. Despite Boyle’s shortcomings, he knew what he was doing when he made 28 Days Later, and it seems more than reasonable to assume that he wanted Jim’s shouting to sound like Miguel’s.
(If you’ve heard the song M1A1 off of the Gorillaz debut album, you’ll have noticed that they sampled the hell out of this scene.)
It’d also agree that Romero meant to visually reference Caligari.
As to your third observation, I’d totally bet it’s coincidence.
Watching the opening 10 minutes you linked, I’m reminded of why I was so disappointed in this movie. Par for the course, for me, when it comes to Romero. He has these genius sequences where he’s deliberate and purposeful, and creatively frightening (the hands out of the bricks! awesome), he usually has a score that, at least for the time it was made is interesting and forward-thinking, but… Then he has bonehead characters who make absurd decisions, or cardboard stiffs who don’t resemble anything close to a believable human being. The great shoe-string-budget practical effects almost make up for it, but in the end I’m always left cold by the failures in the plot and people.