The most curious ability of SCP-1054 is its apparent ability to cause people to die through various means.
These generally tend to involve the person being “unworthy” of continued existence.
I rolled my eyes at these (it just seemed a little cliché to have something that kills things it doesn't like: See overdone SCPs 3. )
It is believed, going on information from interviews with SCP-1054, that it gained this ability from another piece of technology developed by the researchers that originally created SCP-1054 itself (see Interview 1054-1).
Surely it would be in the Foundation's interest to find this technology. Also I don't really understand how an AI could change the hardware in a PDA to function in the way it needed (killing people around the world). A PDA can read and record information, and so an AI program running on the PDA could take advantage of that to express itself. Killing anyone, anywhere, seems a little OTT. AI is software running on hardware. Broadcasting "integrated" hardware isn't feasible (but then neither are most SCPs).
Anyway, since the AI "can take advantage of audio-emitting or recording devices", what about SSTV? Could the AI use SSTV to transmit itself to a receiver?
Currently, it seems your AI is some kind of god machine which sees everything and passes judgement. I think it would be better if it wasn't "kill anyone anywhere", but perhaps an effect caused by it is stronger around wireless Internet devices. Since most people use the Internet nowadays, giving some kind of real, physical threat to the Internet would work well as an SCP, I feel.