Vegetable diseases

I have several diseases that I need to work out and I'm just wondering if there's anyone who has an idea of the conditions I'm dealing with.

Potatoes: Small black specks on leaves, not large or 'rotten' like blight. I do have pictures but I'm not sure how to post them on here!

Broadbeans: These have rust - any ideas how to combat it organically?

Carrots: Some have red leaves rather than green (only one or two)

Tomatoes: Wrinkled leaves (possibly due to under watering?). My stepson also says they have roots growing on the stems

If anyone can help I'd be really greatful

 

@Hywel Griffiths
Rust on Broadbeans is unsightly,but tends not to affect yields.
Discoloured leafs in carrot can be caused by carrot fly, need to keep the carrot fly off with fine mesh or similar.
Tomato leaf curling can be caused by cold nights although this year a lot of tomatoes have not been growing well because of the cool dull weather. Roots coming from the stem are fairly common in tomatoes and not a problem, you can plant tomato plants quite deep and take advantage of these roots.