From my observations of and conversations with trainers, I identified a few of the largest issues that people have with the game.
Despite the existence of third party apps in order to make the game enjoyable, trainers do not seem to mind that these activities are done in a separate app. It is merely a slight annoyance of having to switch between apps while playing.
Bugs
Almost every trainer I spoke with complained about the fact that Pokémon Go has a huge number of bugs that get in the way of playing the game.
Many of the worst bugs have to do with the gym system, which is when it is most critical for the game to work. When doing a raid, thre is always a time limit, and it is frustrating for trainers who can't participate simply because their app is hitting an error.
Another frustrating bug is GPS errors. During my observations, there were many times that trainers were at a raid but had to leave the building or walk away from the gym to try and get their app to find the correct location and allow them to interact with the gym. Not only is this difficult for the individual trainer, but for raids there are always other people who are waiting, some of which often have other obligations that they need to get to.
Unequal Playing Environments
Different Pokémon show up in different places. This can be because of weather, biom, or just random chance. However, it leads to trainers in certain areas having better access to stronger Pokémon.
For example, one trainer told me that they had to go to Israel for work during one of the events, but because they weren't staying in a city, they couldn't participate at all. Situations like these are common in the game, making people in certain locations unable to enjoy it.
The biggest difference between regions is that there are some Pokémon that are only available in certain regions of the worlds, or only a single country. However, the trainers that I talked to seemed split on the matter. Some felt that this was unfair to expect people to travel around the world to catch Pokémon. However, others felt that it made the game more exciting, and gave them a reason to try and explor new areas of the world.
Lack of Information
The fact that there are so many third party apps to help trainers fully take advantage of the game clearly demonstrates that there is a problem with the game itself.
Many trainers that I talked to stated that without these third party apps, there could be a really good Pokémon a block away, but they wouldn't have any idea it was there.
This also ties into the difficulties of starting as a new player, especially if the user has never played a Pokémon game before. There are so many new things to learn, and the game does not explain most of them. Also, a lot of the features are difficult to find, so users can play a lot without knowing they are there.