Some employment agreements explicitly prohibit outside work - in some cases, of any sort at all. Your current employer could fairly presume conflict of interest if you are also doing web development of your own, since strictly speaking that business should be routed through your employer.
One practical issue in all this is that the mental bandwidth that you're consuming on your side jobs is being subtracted from your capacity within your day job. You might literally have 'time', but not all time is created equal. After you've been working 8 hours the extra work is not getting the same quality of attention. If you work Sunday night on your own project there are some Mondays you'll come in half-dead.
The counter-argument is that the side work has you working with tools or more aggressive problems that your day job won't touch. In such circumstances the skills you build will 'expand your reach' within the more normal job duties. However, not all work has this quality.
If you do this at all, avoid largish projects. Focus on something that is small but technologically 'rich'. Focus the side work on things you're not doing 8-5. Don't spend most of your evenings and weekends on these projects - keep every other weekend and most weeknights free. Avoid anything that has a strong support component to it, where they might be messaging you in the middle of the day. It's probably safe to say you already know this.
Also assume your boss will find out in a matter of weeks. You may be thinking there's no way anyone you're working with interfaces with anyone he's working with, but you'll have to count out all the programmers groups, soccer games, and other opportunities for social interaction where the conversation runs something like this: 'I'm trying to find web developers. Know any?' - 'Oh yeah, I have someone working on my little project, here's his card'.
The best thing to do is figure out why your employer doesn't like moonlighting, then see if you fundamentally agree with their rationale.