MYTHBUSTED
A lot of people like to focus on Bill's mistakes when talking about him. Even if these people are fans of his character, they frequently reuse plots like the teleportation accident and the mistake he made with his costumes to portray him. So, for this part of the site, the researchers at Keeper would like to discuss the wallbangers — the moments where you just want to plant your forehead into a wall over the things Bill does.
The Teleporter Accident
Everyone knows what happened. Bill, using the teleporter, merged himself with a Pokémon and needed help to change back into a human. We've seen it happen in the games and most of the manga, and it's the most common element about him that people include in fanfiction to introduce him.
However, it should be noted that this was an accident. It's not completely clear how it happened, although Special gives us one possibility (where his shirt tail got caught on the door, resulting in it shutting behind him). Either way, it's very clear that he didn't intend on doing that, as one can tell by the fact that he begs characters to help him reverse it. For this reason, it should also be noted that this has nothing to do with his research methods, and he probably wouldn't intentionally do this to himself again.
This leads into the second point. Even in the Pokémon world, human DNA isn't meant to change so drastically. Bill is well-aware of this fact, which is why he tries to find a way to reverse it as quickly as possible. Keep in mind that "rewriting" DNA carries a lot of risks; to make it very simple, he's very lucky that he became a Pokémon that could actually function. Sure, Pokémon is a light series, and as such, canon probably wouldn't let Bill face serious risks. However, Bill is also fairly cautious in at least one canon (namely, Special, where whether or not his life is in danger isn't an unusual topic for him), and he most likely understands that he could have just as easily become a Brundlefly-style mess. As a particularly cautious individual, it's also pretty unlikely that Bill would try to repeat the transformation on himself until he was sure it was 100% safe. (In most cases anyway. Zenshou seemed willing to try a second experiment, but the games and Special seem happier staying human.)
With both in mind, does this mean Bill is stupid or twisted for accidentally merging with a Pokémon? No, it just means he's clumsy. He didn't intend on transform into a Pokémon, and he couldn't have possibly foreseen that he would stumble into the teleporter and become one anyway. Basically speaking, it just sort of happened.
The Costume
The second thing most people bring up when they think of Bill in a negative light. To make a long story short, in the anime, he dons costumes to understand what living as a Pokémon was like — as in, he's roleplaying or engaging in hands-on learning. Fairly understandable.
However, during his experiments with Kabuto, he also neglected to realize that the button for his Kabuto costume was also out-of-reach for his costume's hands, and as a result, he became stuck inside it. Also as a result, fans tended to use this as evidence that Bill isn't quite as intelligent as he claims to be.
On the other hand, no pun intended, there's a very important question one should consider when using this argument. Bill lives alone, in a lighthouse far away from civilization. As far as anyone knows, only one person comes that way on a regular basis (his cook), and that person doesn't even actually exist in the original Japanese. So basically, Bill is the only person around for miles — no assistant or anything. So, who would try on the costume before he tests it himself? Sure, there's the argument that he could have tried just the arms and front, but also keep in mind that the entire suit locks together and that, because of this, the best way to understand whether or not the arms work properly would have probably been by just putting the whole thing on to lock the arms in the place they'd normally be in.
The Dragonite
Another supposed facepalm-worthy moment from the anime. People frequently question the fact that Bill, a famous Pokémon researcher, can't identify a Dragonite. This becomes even more frustrating when, in the next episode, Ash's Pokédex mentions Dragonite by name.
However, remember that the anime is also running on cartoon physics. First, it should be noted that the cry Bill recorded sounds nothing like a Dragonite's call. This is important because Bill is essentially identifying the Pokémon based on sound only; as a Pokémon expert, he naturally wouldn't be able to match the call with anything he knew because it literally doesn't match anything to date.
Keeping in mind that Bill is running on sound identification alone, remember that he also specifies when the Pokémon comes to his lighthouse: only on dark, foggy nights. In other words, his vision is completely impaired. Thick enough fog would most likely obscure pretty much any object as it was, but the fact that it was a dark night only made it harder. (The lighthouse's beacon could only do so much, especially given the fact that it was using colored light, not a normal beam.)
So why can we see a Dragonite silhouette if Bill can't actually see it? Because the anime is a cartoon. As stated a couple paragraphs above, the anime runs on cartoon physics, and as such, there are times when a scene in a room that's normally pitch-black might actually just show all of the characters in a darker hue or completely dark blue or something of that nature. This is because as a visual medium, you just can't have action going on in a way where the audience can't see what's happening (unless it's absolutely intentional as a gag). So we can see a Dragonite looming near the lighthouse, but Bill can't. At most, he probably sees a vague shadow thanks to the beacon or hears it draw closer, but it's very unlikely that he'd be able to see enough of its shape to figure out that he's looking at a giant Dragonite.