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I haveTumbler tomatos in a hanging basket which are starting to fruit. I'm thinking all looks good when I then noticed that black spots have appeared on quite a few of the leaves. Should I be worried. Any comments.......   newbie

Where are you baskets hung up? In/Out?
This time of the year you would usually see black spots if the baskets are over watered and/or kept in humid conditions...if it is grey mould..you just pick effected leaves off and give more ventilations (if in) and ease with watering and try not to shower your plants when watering. Usually plant will recover from grey mould if the humidity issue is sorted.
It is not quite time of the year for blight yet..thats another possibility..if it would be that, which I doubt, you would see it rapidly spreading all over the plant and not just leaves. That is more serious..you can still slow it down by removing affected leaves. There is commercial sprays about for fungal problems..but its up to you if you fancy that sort of thing.
If you plants are out...could cold have affected you plants?

They are hanging out and I guess I have been keen to keep them watered and have been showering them as well!! Last lot was yesterday when I included tomerite. I think that maybe the answer, I'll cut back and pick off the spotted leaves. My first babies - was all worried  ;D

 ;D...don't wet the 'baby's' head..just keep the 'toes' washes.. ;) ;D

Does the leaves look like this

Looks similar although mine are slightly widespread on the affected leaves. Covers more of the leaf. I do have a photo but not sure how to post it and show you. 

If its simular to the photo then you have been watering in full sun and the water droplets magnified by the sun have burnt the leaves.

Figures!  Well that's another lesson learnt !!  Thxs for the replies

If you just get tiny black spots... like the small ones in the photo... don't panic it seems to be a tendancy in small toms... or a reaction to being grown in baskets... that has no real impact...  :-\