Not mosaic virus. I'm thinking what you have is bacterial leaf spot (BLS), one of the more common diseases of peppers:
http://www.ctahr.hawaii.edu/uhmg/FAQ/FA ... epper2.jpg
It is difficult to do much about it, once they have it, but you can work on prevention:
http://www.gardeningknowhow.com/edible/ ... eppers.htm
Crop rotation can help prevent bacterial leaf spot. Do not plant peppers or tomatoes in a location where either of these crops has been grown in the past four or five years.
At the end of the season, remove all crop debris from the garden and destroy it. Do not compost plant debris that may contain the disease. Once the area is clean of all visible debris, till the soil or turn it with a shovel to bury any remaining bacteria.
The bacterium is spread by splattering damp soil onto the leaves. Reduce the splatter by using a soaker hose and avoiding overhead watering. Stay out of the garden on wet days to avoid spreading disease on your hands and clothes.
Bacterial leaf spot is also spread through infected seeds. Buy certified disease-free seeds and seedlings. Itâ€™s best not to save your own seeds if you have ever had a problem with bacterial leaf spot on peppers.
I noticed your soil is not mulched. I always recommend mulching. It conserves soil moisture so you don't have to water as much, it keeps the soil cooler in hot summer areas, helps suppress weeds, the mulch eventually breaks down to feed the soil AND it helps prevent soil splash back, so helps prevent disease.
Since you know you have the disease in your garden now, you can look for BLS resistant varieties to grow in the future.
Here's another article about it:
http://vegetablemdonline.ppath.cornell. ... afSpot.htm
Warm, wet conditions are favorable for diseases caused by bacteria. Therefore, irrigation method is an important consideration in managing BLS in the field. Overhead irrigation provides both a means of spread for the pathogen and favorable conditions for disease development, therefore trickle irrigation is recommended. In addition to movement by splashing water drops, the pathogen can be spread through any mechanical means imaginable when plants are wet, including on workerâ€™s hands and on machinery such as cultivators. If possible, avoid working fields when the plants are wet and work infested areas last. Disinfect machinery used in infected sections of the field after the job is completed.
Low nitrogen or potassium, and extra high magnesium and calcium levels have been associated with increased crop susceptibility to BLS. Pepper crops that show visible signs of nitrogen deficiency (light colored leaves) have been severely affected by BLS in Connecticut. Researchers have also found that BLS is more severe on pepper plants grown in soils adjusted with dolomitic lime, which is high in magnesium, than plants grown in soils adjusted with Cal limestone (CaCO3). Maintain nutrients at the proper levels (moderate to high) to help plants resist infection
The bacterial leaf spot does infect a number of other plants including beets, so it well could be what is bothering your beets as well.
Bacterial and fungal diseases of plants are much better prevented than treated. Most "treatments" do not work very well once the disease is well established. Along with mulch and making sure there is good air circulation, things you can try include spraying (including undersides of leaves) with baking soda solution (a tablespoon of baking soda, 2 1/2 tablespoons of vegetable oil, a teaspoon of liquid soap, not detergent, to one gallon of water), treat with copper fungicide (although this one is not a fungal disease, the copper solution is said to work against it also). There is a product called Serenade which uses a strain of Bacillus subtilis to fight bacterial and fungal diseases. It is completely organic and harmless to insects.
We would have no way to tell by looking at your pictures whether your soil is alkaline or acidic, but you need to know. Either send a sample to be tested or buy a pH meter (the kind with long probes). Any condition which stresses your plants will make them more vulnerable to whatever diseases or pests are around.
Whew... probably more than you wanted to know, but hope it helps!