The individual will end up overpaying on social security and underpaying on most other taxes. When they file their taxes for the year, they will most likely owe some additional money to the government. As long as they pay it promptly, I don't think the IRS will have any issues with the situation.

They can also request that the employer withhold additional taxes; this is fairly common because of situations where both spouses work.

They likely have two healthcare plans, but that's generally not an issue - again, it's fairly common if both spouses are employed.

For the 401K, the individual will just have to make sure that their total contributions between both companies are under the federal limit.

It’s not illegal to have two jobs.

The US system is setup such that employer A doesn't see any information that would reveal employer B.

The IRS knows but they don't tell employers.