Technics SL-1300G Turntable issues

Take a short level and place it on different parts of the platter. Rotate the platter a quarter turn at a time and if your level bubble is in the middle through the entire rotation, it's spinning flat and you're good to go. As to the looks of the side of the platter bothering you... nothing is perfect in our world unfortunately.

@faustuss  

You are going the wrong way about it, the stylus runs on the platter not on the base.

@faustuss 

Sorry you don't understand the fact that the platter is the part that really needs to be leveled. Of course you start with the base but if the platter is not leveled after leveling the base, you need to adjust the feet until you get the platter leveled.

On a quality TT like my VPI Classic the level of the base is identical to the one of the platter. But on lesser quality TTs like the Pioneer DX1000, or Pro-ject debut, I had to make legs adjustments to get the platter leveled. 

Luckily the VPI Classic can handle heavy center weight and outer ring. I use them for every record I play so they are pretty flat. If you truly want hifi results, this vinyl thing can be tedious. Tone arms / cartridges alignments and specially the cleaning vinyl and storing  part. Not for everyone. 

I just checked your system and you seem totally committed to vinyl. It is very easy to check a platter for proper level. Just use an eye bubble type level and move it around the platter and check that the bubble stays dead center in the eye. Then move your platter to multiple positions and repeat the bubble test. Once you have made a 360 platter revolution and all positions had the bubble centered, you know your platter if leveled and spinning without wobble. However that was not the OP's concern. His concern is over the side of the platter having lines that are not uniform as platter turns. Anyway that was my understanding.