​I know that it's bad to wash your car in the sun, so I try and avoid it as much as possible.  Sometimes the sun will appear whilst your mid washing and do it's thing, and ruin everything. 

What I've notived though is that sometimes there is visible hazing left over afterwards (despite me using 2 buckets, wash mit etc.) and sometimes there isn't, as if they've now disappeared.  Is this caused by the way the shampoo has dried, or due to the sun softening the paintwork making the likelihood of hazing/swirls even greater, or just the angle it's viewed from?

I'd say if you're not rinsing with clean water after you've washed it then it will be the shampoo drying. Best bet would be wash the car then go over it with an open ended hose as this sheets off better so leaves less water marks

Interesting one.  A couple of things to try, if it were me.

 

1. Shampoo: does it have additives/waxes/polymers? Try another shampoo without these?

2. Try a water filter setup to improve the wash process and minimise watermarks in general.