Kaveman The timegrapher should show a flat line with low beat rate (+2 to -2 a day), good amplitude (about 240 to 280), beat error (0 to 0.5) and lift angle (50 to 52).
If you are getting anything different is a problem in the movement. From what you are saying, my guess your balance wheel pinion is not swinging in an even angle/height from the pallet fork.
The simple test for height is when you place the watch dial facing down and very slow move side ways and upwards. If your spring have a height issue the balance wheel will stop.
If it is swing angle you should be able to see from the timegrapher line. Anything that is not a flat line is usually not good for the watch.
There is also a possibility where your watch may have a loose escape wheel as well. Sometimes an unserviced watch will have the escape wheel grinded bald against the jewel. A good quality movement will have an incabloc to act like a shock absorber for the escape wheel.