Personally I don't care for the disk model. Even though it is able to answer some questions well, based on my traveling experience, I prefer other models which better explain my personal real life experiences.
Can you describe any of your personal real life experiences that the conventional spherical Earth model cannot explain satisfactorily?
The best thing I can do is advise not come here looking for failures in the spherical earth model. There is only one and it's been thoroughly researched. Whereas there are a lot of models and different answers/explanations for observations within those specific models.
It's best to come here with an open mind and look for evidence that, on some level, does one of two things:
1. Provides an alternative to the claim that ______ observation proves the earth is round.
2. Provides evidence of observations which can weaken any aspect of the round earth model.
If you would like I can give you some. It's important to understand that there is evidence which casts some doubt on existing systems. RE people, because of conformation bias, will say that this evidence proves the earth is round. FE people, because of conformation bias, will say this evidence proves the earth is flat.