Random broken blood vessels all over during pregnancy?

Fairly common. Dilated and broken blood vessels occur pretty commonly during pregnancy. They often go away after baby is born. Discuss with your ob.
Will improve. These are result of change in hormones and will decrease after delivery. If they do not resolve after delivery they can be easily treated with laser or even electrosurgery. It is best to wait a few months after delivery to see how many resolve. If however any are bleeding, isolated lesions can be treated with electric needle.

Related Questions

I have green veins showing on hands wrist and legs. This means? If you have negative pregnancy test urine and blood after sex with light period.

Normal. vein color can vary with indiviuals. The color is usually bluish but can appear greenish based on your skin tone. Read more...