A bit of general lawn care at this time of year will improve it - without too much effort. I expect from your description that the grass is quite mixed in type, but that isn't really an issue unless you want the 'green at the18th hole'. I moved to my current house a coupe of years ago. The front grass was compacted and largely buttercups, dandelions, daisies and moss. I've only fed it, used a weed and feed each spring and cut it regularly. It's now grass with only the odd weed - mainly seeding from other people's gardens - and looks very good.
If you have any dips in the ground, it might be worth filling them with some topsoil/compost and re-seeding there. I don't aerate mine, although it would benefit from that, but if your ground is compacted or waterlogged I'd suggest you do that. Take a garden fork and spike the ground to a good depth over the whole area. Grass needs air to thrive. You can brush sharp sand down the holes to help drainage too. If it's really bad, you can buy a tool for that which removes plugs of soil to make bigger channels. Regular cutting is vital - every 5 to 7 days through the season. That way, you encourage healthy growth. Hope that's of some help