The solution seems counter-intuitive: don't spend too much time lingering on Deadpool himself. Yes, obviously the film follows Wade Wilson. That's true. Before his cancer and the ensuing experiments to activate his mutant genes, he was still going at about forty jokes per second. However, in those moments, he does come off as surprisingly human. As a mercenary, he appears to have a soft spot for victims who hire him for revenge. He falls in love. He even becomes afraid and angry in a very naturalistic fashion near the end of the experimentation portion of the story.
Director Tim Miller (in his feature film directorial debut) wisely recognized that as a character, Deadpool is not particularly strong enough to carry an entire story by himself. He is at his best, most interesting, and most entertaining when in context of other characters. Too much Deadpool at a time, and you risk the non-fanboys getting annoyed by his increased sixty jokes per second. Miller avoids this through two key techniques.
First, he jumps around. The film opens up in the "present" as Deadpool is trying to track down Ajax (or, Francis rather), the man responsible for torturing him, activating his mutant gene (which is a super healing factor), but also causing his body to become covered in tumors and lesions. Basically, he's pissed that he went from the super attractive Ryan Reynolds to what appears to be "an avocado that had sex with an older, uglier avocado," as stated by Wade's bartender friend Weasel (TJ Miller). After a humorous and violent action sequence, Tim Miller then cuts back to fill in the blanks.
It works in part because Wade Wilson is less annoying and more interesting than Deadpool, so it gives us a reprieve from the hugely immature nature of his superhero alter-ego. Generally, jumping around through time is not ideal. However, Deadpool also breaks the fourth wall. A lot, actually. Eventually it cuts to him in the present, addressing the audience in order to fill everyone in. Going back to the beginning also works because it helps fulfill that side of the character. It feels less like poor writing or directing and more like part of the joke that Deadpool knows he's in a movie and he's being watched.
The other thing that helps Deadpool become more easily digested by a mass audience is that they pair him up with two X-Men: Colossus and Negasonic Teenage Warhead. The former is pretty much a stand in for your traditional, goody-two-shoes superhero. He's the "ideal" hero trying to recruit Deadpool to that side of the super people spectrum. The latter is largely there for the sake of dated pop culture references and kind of sexist and/or ageist jokes. (I'll actually address that in a moment.) These characters actually have a fair amount of screen time, and are a sizeable part of the final action sequence. This allows for more of that typical widespread action we expect in these movies, but it also places Deadpool in the context of your pretty traditional superheroes. Pairing Deadpool with someone playing it straight is critical to the success of the character, as it allows him to bounce off someone. This is why the best Deadpool comics are ones where he's part of a team (like X-Force) or paired with a character almost completely void of humor (Cable & Deadpool).
So just to touch a bit on the humor itself: you probably won't have to dig hard to see people criticize the film for its occasionally sexist humor, or its ageist jokes, or its weirdly outdated pop culture references. These things all exist within the film, absolutely. The thing about Deadpool though is not that he is always funny. It's that he thinks he is. As a character, he has always been about saying all the jokes and thoughts that come to his head. He'll spray them everywhere just to see what sticks. This is true in the comics, in the games, and definitely in the film. Almost every line he has is a joke, and they can't all land. Most don't, actually. But that's not the point. Deadpool is a crazy guy who has no filter. That's his characterization. That's why he's one of the more annoying characters, and why you need him to be paired with others for sustained success. You don't want him to annoy the audience; you want him to annoy the other characters while the audience watches with amusement.
As for the outdated references? Well, yeah, that's also a pretty big part of your typical Deadpool comic. These factors don't make him an easily accessible character, really. But it is what makes him unique. The film does a pretty great job capturing those aspects of his character. The fourth wall breaking might actually be where the comedy succeeds most, which would also be fairly similar to your typical Deadpool comic.
Not everything works in the film, of course. The conclusion of the Wade/Vanessa storyline feels a little strange. Deadpool's history is rooted in negative stuff happening, so it's kind of strange seeing a happy ending. (They probably did this just to make a bad "happy ending" joke, now that I think about it.) It's a bit strange of a decision though because that's a character they'll now have to keep track of going into the sequel. They'll have to account for this person whose only role was to be the damsel in distress and/or love interest motivator for the hero. It's strange too because perhaps the one thing they didn't exactly get was just how literally insane Deadpool is. Throughout the film, he's regularly addressing the audience. In the comics, though, he almost always has conversations with himself and his inner monologue. That's quite a difference, really. Breaking the fourth wall like that doesn't make him seem crazy. Arguing with the voices in his head? Kinda does. So it seems strange that they would keep around the person that grounds Deadpool. She's an important character because she does that in this film. She gives the film a surprisingly solid emotional core that definitely helps make the film as good as it is. But practically speaking, she kind of has to go.
The other thing that didn't quite work for me was his team of sidekicks: Blind Al and Weasel. Neither character really gets to do much but crack a joke or be the source of one. It would have been cool to see a more capable Weasel - the weapons buyer from the comics - actually helping Deadpool in a meaningful capacity other than just "emotional support." The jokes makes sense - TJ Miller is a hilarious comedian. But neither he nor Blind Al are allowed to really do anything. I'm not sure if they kept them on the sidelines because they already had Deadpool teaming up with Colossus and Negasonic Teenage Warhead, or if they just sort of forgot about them. Those characters don't often help him in the field, but they do help him plan and prepare.
Other than that, I thought the action was really good. It was violent but not gory and super graphic. And they used the violence as comedy in some really effective ways (that sounds weird, I know). Sometimes there's a little too much "bouncing Deadpool," and that CGI doesn't look all that great at moments, but most of the time it was fine. The suit looked good and Reynolds was pretty great in the titular role. The sequences between Colossus and Angel Dust were also pretty fun. It was cool seeing some actual heavy hitters duking it out.
It's hard to keep track of all the fourth wall breaking and all the Easter eggs in the film, but that highlights how well they actually got the character down. So if you're a hardcore fan of Deadpool, I don't see why you wouldn't enjoy the movie. And if you're more of a casual fan (like me), it's irreverent humor actually feels surprisingly fresh in the world of far-too-serious-for-their-own-good superhero movies. (Seriously, the trailers go from Batman v. Superman to Captain America: Civil War to X-Men: Apocalypse and it's like, Christ, lighten up, guys! It's starting to feel a little like we've moved into the late '80s era of superhero comics, but in film form.)