Current Mt. Rainier resident (though selling soon because of school issues, which I won't belabor) - we've been here almost 9 years. Crime in Mt. Rainier is mostly (stress on the word mostly) confined to the large apartment complexes (break-ins, muggings) and the town center area (crimes here are mostly public drunkeness, disorderly conduct), near the bus stop.
Outside of those parts of town, the majority of the crime is thefts from vehicles. To be sure, there are muggings, but those typically happen late at night (after midnight) (I base this on reading the crime reports from the city's Chief of Police:
http://mrpdchief.blogspot.com/ ). I believe the arsons mentioned above were solved and I don't recall any recently. I regularly walk the dog in the neighborhood, walk to the bus stop to get to work, and take my son on bike rides through the area.
It is a safe neighborhood, but like any urban area, one should be sensical - i.e. don't go walking alone at 2 in the morning. As a general rule, streets on the north side of route 1 tend to be more desired than those on the south side (nicer houses, bigger yards, less cut through traffic).