How to ensure my device is safe for every day use?
If this would be a professional design you would do an FMEA, for Failure Mode and Effect Analysis. Consultants in suit and necktie offer you expensive FMEA workshops, but it's all just common sense. Throw him out. 

Organize a creative session with also other people than the designers present. You want to think of any possible thing which can go wrong with the product. The designer must be present to answer questions, but she's not the best person to do the assessment: every designer thinks her design is failproof, and issues overlooked during design will also be overlooked during the FMEA.  

When you have listed up the things which can go wrong (that's the failure mode part) you add columns for Occurrence Rating (OR) and Severity Rating (SR). How likely is the failure to occur and how bad would it be if it happened. If the result of the failure is that the lights in the den go out that's a lower severity (1) than when the house would burn down (10). The product of OR and SR give you a Risk Priority Number (RPN). Sort the table by RPN, high to low, and you know which issues you have to attack first.  


 OK, that sounds like complicated, and no fun at all. For a hobby project you don't want to do all that, then you can better switch your hobby to knitting. But the principle remains: try to assess what can go wrong, how bad it would be if it would, and what you can do to prevent it.  

The fuse is a simple solution to a lot of possible problems, and that's why you'll find one in most products. The fuse should be the first part viewed from the mains. Don't place it between the power supply and the circuit, because it won't protect the power supply itself (unless that already has a fuse).
If heating up is a risk, you can provide a heatsink (which you would probably need anyway to keep the FET within specs). If you want extra insurance add a thermistor, which you use as an overheating detector to switch off (part of) the circuit in case of overheating. Note that for instance voltage regulators often have thermal protection built-in, so for those you won't need the extra temperature sensor. 

For more we'll need more details about the circuit, but overheating and overcurrent (short-circuit) protection often covers most of the critical failures.