An Update to the saga that started here and continued here.
Now, the phone (a Motorola Droid 4) is running Cyanogenmod, to be precise the "stable" version for this phone, which is 10.1.3, meaning Android 4.2.2.
And I am still seeing the problem described in my earlier posts, namely that an arp entry for a host that can be reached locally is not removed from the arp table when the phone leaves the network for which this is true.
Again, the scenario:
Phone is online in wifi A, host X is in the same network and can be reached without passing through a router.
Phone is moved to another location, where wifi B (no relation with A) is available, so phone connects to that. Phone is now unable to reach host X as phone believes host X to still be a locally reachable host but offline or invalid or whatever. When turning off the wifi (i.e. using 3G instead), the host becomes reachable (as the arp table is specific for each network interface). A reboot clears the arp table and makes normal networking possible again.
As far as I understand the issue, this is not correct behaviour.