If you tighten the nut a bit, you should hold the filter, or the nut at the top end of the filter, with grips or spanner to ensure that the whole unit doesn't turn with the bottom nut. Don't overtighten, a little nip might be enough to stop the leak.
The water loss will result in fresh water entering the system, albeit slowly, but fresh water has potential to deposit scale (if it is hard) and will also be oxygenated, which is bad for steel (e.g. radiators). Best to stop the leak.
If the water in the system is hard, then I would expect the leak to build up a fine scale deposit, which would likely seal the leak in the process.