Granted, the laws of physics and the rules of equal temperament determine that your instrument can never play perfectly in tune all over the neck. But with the right equipment, you can get pretty darn close. In order to be dead on the money, most luthiers recommend using an electronic strobe tuner or equivalent. A regular, inexpensive tuner won't be as accurate. The strobe tunes within one-third of a percent of a semitone.
Old strings can be very difficult to intonate.
Strings lose their uniform consistency as well as attract hand oil and dirt. Frets also put small dents in them. So buy new ones as needed. Be sure to make all other necessary adjustments first. Any later changes that you make will invalidate the intonation process.