I spaced my potatoes about 3 feet and between each I would like to put about 3 tomatoes to save space. Will this create problems in the near future?
It's harder to control blight when the two are planted in close proximity. Late blight caused a devastating epidemic in the 1840s in the North Eastern USA. http://vegetablemdonline.ppath.cornell.edu/factsheets/Potato_LateBlt.htm
But there are plants that have cherry tomatoes grafted onto potato stock eg. http://www.edible.co.nz/fruits.php?fruitid=77 which I guess is a case of putting all your eggs into one basket.
Anyway, generally, don't intercrop potatoes with tomatoes. It's harder to control diseases if you do.
When it gets hot and humid tomatoes grow fast, and they can block the light to the potatoes which don't grow so big.
In general, try not to mix plants of the same family (and in this case both share Solanum as genus), both for competition on same nutrients (they share similar metabolism), and their can share diseases.
Tomato plants don't have deep roots, so I think you can have problem harvesting potatoes without damaging the tomatoes.
I never had problem with shadow: I don't think tomatoes does so much shadows, and potatoes (and tomatoes) growth well in the shadow of trees.