One issue that can come up is liability if someone is harboring fugitives or giving sanctuary to what could be a criminal group during the planning and preparatory phases of a criminal act.

Safehouses are a security nightmare for coordinators who have to look out for liability in these issues. This can especially be the case if the "fugitive" is not accustomed to living as a fugitive. One homesick person on the run making a phone call "home" can destroy the whole operation.

This means setting policy that respects the privacy of the hosts and the security of the situation along with obscuring the intel value of whoever might be routinely doing hostile surveillance on the safehouse.

Generally speaking:
Landline phones - these are set up with minimum service, if any. There are really two ways to do this, one is either to have the phone practically disabled, or two to have so many people and locations sharing the same phone line that any intel gained from it is going to require huge amounts of resources to sift through.

By practically disabled that means one of the minimum service plans which basically only dials out local calls, and long distance with calling cards. Frequent use of the phone line with different calling cards obscures the intel value of the phone. This is especially the case when you have people speaking on the phone in different languages. I messed with the feds for a while on this by making my landline phone available as a restricted phone (long distance and incoming collect calling disabled) in the lobby of the place I was renting in, so even homeless people could use the phone if someone let them into the lobby. Even a step better can be to set up a cordless phone extension with just the charging jacks in the public areas, that way nobody can stick a lineman's phone recording device on the line from a public area. You clip the wires on all other jacks leading from that main line and only run live jacks to the one phone in the cordless system that runs to the base station.

Depending on the trustworthiness of the people around, expect to lose a handset every once in a while, so the cheap systems are the way to go, the kind that come with three or four handsets.

Another thing you can do is jackwire some neighbor's service on that phone system, especially in an apartment or office building. There are even long range cordless phone systems that can be set up with the main base station in a different building, or at least down the hall a ways.

Unsecure wifi internet is also something that would be available within proximity of a safehouse. Encourage the local bars and coffee shops to run free wifi, and if that is not practical, run it out of the house.

Clandestine residents and travelers should already know how to use throwaway phones, at least semi-anonymous email and other computer commo, and not be pulling really dumb stunts like having mail sent to the safehouse in their own name.

Some safehouses get tons of mail, in the names and fake names of everyone who had been there in the past. One strategy I heard of was that the resident simply assumes one of the pseudonyms of a frequent visitor. Packages can be more risky though, since someone has to sign for them. Obviously you would have to restrict access to people you can trust or assume that packages and mail will get lost from time to time.