Normaly plants accumulate only nitrate. Nitrite is forming by enzymatic reaction or from microbes if you have unhiegenic or bad conditions of the storage of plants which contain high amounts of nitrate. Because nitrite possesses a high rectivity it would react with the plant tissue. Therefore it may react with human food and are able to form carcinogic products.

According to FAO/WHO and JECFA the Acceptable Daily Intake (ADI) is 0-3.65 mg/kg of human weight for nitrates and 0-0.13 mg/kg of human weight for nitrites. 

There are also nitrate limits for spinach and lettuce which are considered nitrate accumulators. Nitrates are not dangerous per se (there is literature that suggests that are beneficial for human health: Hord et al., 2009).

The nitrites that are produced by nitrates are not considered safe because they produce nitrosamines which can cause cancer. 

Nitrate is required by plant for N requirement for producing protein beneficial for humans, however nitrite are not safe as lead to carcinogenic products as said by Ingo and Petropoulos.