Lack of English would certainly be a hint that they lack English. It doesn't offer up proof of their status.
Calling the police or ICE to report that a proposed tenant can't speak English will surely get you on their "crank" listing.
They might though notify the Fairness in Housing Commission which will be on the landlords butt.
The only solution to many of these problems is a National ID issued to Citizens only.
Legal residents already are required to have their Alien ID card.
If the law would allow the landlord to require a proposed tenant show one or the other of those ID's that problem is solved.
The only thing stopping this is our own people who get up in arms over a National ID card.
They of course are also the loudest complainers about the criminal invasion.
They demand the government do a job without the proper tools.