The following quote is from the BBC:
The strike has divided opinions in Rio. On social media, many support the sweepers' demands for better salaries. Others say they are opportunists and the situation is a big embarrassment to the city.
But Brazil's culture of littering the streets doesn't help. A video that went viral online shows that even authorities have a problem with that. Rio's mayor, Eduardo Paes, is seen throwing what seemed to be the rest of an apple on the sidewalk - and now promised to impose himself a fine for his wrongdoing. His government recently created a programme to keep Rio's residents from littering the streets.
I'm wondering what the phrase in bold means.
Apparently it means that the fact that many people litter on the street bothers them.
But I think the word "problem" has nothing to do with bothering or being bothered, does it?
I would say it means that authorities themselves stimulate littering on the streets.
I am really interested in hints to help figure these kinds of things out in other contexts by giving some examples saying "they have a problem with . . ." and to write the meaning.