One key limitation is multicollinearity, which affects the interpretability of results. Moreover, oversaturation in models with too many predictors can result in overfitting. Small datasets, or sparse data, can also challenge the accuracy of logistic regression models.
I'd argue collinearity isn't really a problem except in the sense that you may have too little data to make inferences about unique effects. For example see https://janhove.github.io/posts/2019-09-11-collinearity/
Overfitting isn't really a specific logistic regression issue - but can be a problem for any model with many predictors (or if there is hidden selection from a larger set).
Generally I'd worry most about:
- independence of observations
- linearity on the log odds scale of continuous predictors
- complete or partial separation
The latter is linked to sparsity and small samples. There are fairly good solutions for all of these issues.
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