MoonShadows said
 However, once I try to increase the tempo (slowly, mind you) mistakes start to creep in whether it is crooked bowing, string crossing, intonation or just forgetting notes.

Any suggestions? Thanks.
  

@MoonShadows 

So playing at faster speeds is a separate skill than the bowing, string crossings, and intonation... and will be different from your shifting and vibrato later...

You need to work on all of these areas separately.

1. Bowing - practice in front of a mirror and bow slowly straight on each string
2. Crossing - slowly play each string open, use whole bow on each over and over
3. Intonation - If you are having problems with intonation there are many ways to work on this.  Some beginning students will use tape at first to learn muscle memory (have someone experienced place the tape for you). Work on first position until you are consistently playing notes correctly... then work in other positions.  Play with a tuner to see you are playing in tune.  But keep in mind that players work on this skill for years, continually improving.
4. Playing a tune faster - Always begin slow.  Play at a speed you feel is slow then reduce that another step or two slower. 

Playing faster will always be more difficult than playing slower.  But the things you listed as mistakes should be worked on separately, one at a time for a while. 

Don't feel bad or that you are doing anything wrong.  4 months is still quite early to play well at fast speeds.

Hope this helps.

@HP 

She has awesome vids... and a great learning site.