Does my entity-relationship diagram reflect the relevant business rules?
First - I agree with S4V1N completely on the Category-Business link - you need a table in between, as each business can have many categories, and each category could be tied to many businesses.

However, as the rules are currently stated, I don't think you need a table between City and Business. I think you've got City laid out wrong.

Currently, each business must be in one and only one city, and each city can be home to multiple businesses. For that, the City table should not have a B_ID column, as a city is tied to no one business. (I also see no reason for it to have a U_ID column, as no relationship between User and City has been established. I suspect a cut-and-paste issue.) Business, however, should have a CI_ID for the city it's in.

Also - the way I read the diagram, it looks like each user must have at least one Comment, Rating, and Checkin. The rules explicitly indicate "one or more" checkins per user, so that appears correct. However, it doesn't look to me like the user is required to have any comments or ratings - so shouldn't those two be linked with the "0 or more" connector?