Potato Blight is the main problem when growing potatoes. It is an air bourne fungus type disease which attacks the foliage (and later the tubers) causing it to collapse. It commonly occurs in wet, mild and humid conditions and is difficult to manage. It will affect tomatoes as well, although if they are grown in a greenhouse this will afford some protection as it is mainly, but not exclusively, a disease which affects out door crops. It starts with brown marks on the leaves, image left and quickly spreads so that all the foliage turns brown or black collapses and the plant looks patently sick; it cannot be missed. Once it takes a hold there is not much that can be done as it spreads rapidly.
Good air circulation can help which means not planting the tubers too close together and following crop rotation. This means never growing potatoes where they were grown the previous year, especially as the fungus can overwinter in any tubers left in the soil which if they are allowed to grow the virus can spread from there. This means when clearing the veg plot at the end of the season it is very important to remove all potatoes including any very small ones. In addition you can grow Blight resistant potato varieties, which does not guarantee that Blight will not visit, but very much reduces the chances. Late varieties of potato are more prone to blight so growing earlies and salad potatoes may escape as the warmer humid temperatures are more likely later in the year. In the eastern parts of the UK and drier areas it is less of a problem. It is the humid warm air which allows the pathogen to spread, and it can destroy a crop in a couple of weeks.
If the plant becomes badly infected the only possibility is to cut off all the infected leaves close to soil level and be careful to pick up all bits of infected leaves. If the blight has not reached the tubers they can still be harvested later, if the blight occurs later in season, so the tubers have grown sufficiently to make a decent meal.
There are also varieties offered for sale by garden centres and on line which are more resistant such as Sarpo range and it certainly worth looking at this range if growing maincrop which will mature later.
Potatoes also suffer from keeled slugs which live underground and bore into the tubers, which damages them and makes them prone to rotting. Because this form of slugs lives so far underground slug pellets are not effective, nematodes are a better suggestion.
Potatoes also get scab which makes them look unattractive but they are edible and not noticeable when peeled. This tends to be more of a problem on thin chalky soils which are prone to drying out the addition of organic matter will reduce the risk of scab.