Suppose for this scenario that the restaurant is very strictly vegan (and in a region where veganism is truly understood), and there is no wine present. All dishes that the restaurant uses are strictly vegan.
I can think of a few problems, but I am hoping that someone will be able to spell out these problems in detail with sources.
An initial list of problems:
1) Keilim were bought used and were used in a treyf restaurant
2) Bishul akum
3) Indirectly benefitting from a Yehudi's melacha on Shabbes There could be a Yehudi worker who works there on Shabbes (for a kosher diner eating there during the vokh, would this be considered a violation of the issur against gaining hano'ah from a Yehudi worker's melacha on Shabbes?) or a ba'al yehudi of the restaurant who keeps the restaurant open on Shabbes (same question: would eating there during the vokh be considered a violation of the issur against benefitting from a Yehudi's melacha on Shabbes, albeit indirectly)?
Can anyone elaborate on the potential issues above-- if they are indeed issues or if they are not (and why or why not, with textual support)-- and do the same for any additional potential problems that I did not list?
Thank you for your help!