You noted the most egregious error — the failure to show the whole Roman Empire as Christian from 380 onward — but it also missed the spread of Christianity into and across central Asia by the Nestorians prior to the rise of Islam, the spread of Buddhism to East Asia (and among the Mongols among whom it for a while displaced both their native shamanism and Nestorian Christianity), and the Christianization of the Russian Far East, including Russian Alaska.
Indeed. They fail to note the spread of Christianity by Thomas in southeast India, as well, nor the predominance of the Hindu way on Bali, and Christianity on west Timor and elsewhere, or Judaism in concentrations throughout the Mediterranean, nor animism, nor Zoroastrianism - or just simple monotheism. The map lacks small scale sweeps and granularity.