What can be done to improve the guitar

A good guitar should play in tune, and a few fundamental checks will tell you if your guitar needs attention. Depending on what is required the costs to fix it will vary, and may even outweigh the value of the guitar.

This is best done with a good chromatic tuner. Make sure you have relatively fresh strings. Start by tuning the open strings with a tuner and then check the harmonic at the 12th fret. This should be in tune regardless of fret positions, scale length etc. If it is not in tune suspect the string and try changing it for another.If all is well, then play the octave of the open string at the 12th fret. Again this should be in tune. If it plays sharp then more compensation is possibly required at the saddle, or the fret could be in the wrong position. If it plays in tune then it is now time to check the notes at the lower end of the fingerboard. Play the first fret and check it with a tuner. If it is sharp then compensation may be required at the nut or it may also be a fret placement problem.  Accurate measuring equipment is necessary to measure fret placement and this is generally not possible at most homes or studios.

Repeat the testing procedure for all the 6 strings and keep a note of what has happened. If your guitar checks out Ok then good, if it has problems then it may be necessary to take it to a good repair person for rectification. Each string will probably give you different results as each string has different physical properties.

If you do attempt to alter things at home at least do so on a spare nut or saddle, so if you make a mess of it, it is no drama to put the old nut and saddle back in place.

The saddle is sometimes thick enough that it can be shaped to alter the "break" point of the string. For the best results this adjustment should be performed on each string separately. If the string plays sharp at the 12 fret and you are positive the fret position is correct then you can file the top of the saddle to move the break point further towards the rear of the guitar. If it is flat  then you can file the saddle to move the break point forward towards the nut.

Nut adjustment is best left to an experienced person as both the length and the height need to be set accurately.