Bike directions, Google says, are in beta. Google's released a lot of stuff into the world as a beta and most of it has been pretty usable right off the bat. The bike directions have a few issues, but it's hard to blame them. It's a hard task. I'm going to focus on Chicago, as it's a city I know and Google seems only to be seriously trying in cities (probably a good decision).
The biggest challenge of generating bike routes is that there are so many different kinds of bikes and riders. I once thought a good way to do it would be to collect lots of data on the characteristics of various streets and let users set their own priorities (bike lanes/wide right lanes, traffic volume, speed, surface, etc). Someone that's not all that experienced and rides a mountain bike or hybrid or something won't mind dirt paths and weaving around through side streets but will freak out on a major road. I have a road bike with skinny high-pressure tires and regularly biked to work (and just about everywhere else) for a couple years in Chicago; I want to be going straight and fast on a road that gets favorable light timings. Since riders like me can figure out our own routes, they probably did the right thing by catering to the novices. I worry a bit that if people start thinking Google's routes are really the most efficient ways to get around on a bike they'll become pretty discouraged with urban cycling. Like John Forester points out in Effective Cycling, beginning cyclists are often advised to do suboptimal things at first and become discouraged and quit completely before they ever learn to do it right.
The worst thing Google does is set you weaving on side streets. Not just ducking off a major road for a while, but literally going block by block turning left, then right repeatedly. It's hard on your mind to remember all those turns, and it's hard on your body to repeatedly stop and accelerate. The question is whether cyclists will graduate from Google's routes to the realization that they should just get on Damen and go, or whether they'll putter around, get tired, and give up. Often the routes ask you to cross or make a left onto a major street where there's no light. This is frustrating even in a car; it's near impossible at certain times of day on a bike. A few experiences like that could be enough to really sour a novice's impression of urban cycling, where if the same rider had been on a major street in the first place he'd have had no problem. Some of the cases where Google does this are baffling. In one route I generated, you're on Chicago Ave. headed west and you eventually want to go south on Cicero Ave. So, naturally, you just go up there and turn left at the light, right? A few blocks before you get there Google diverts you south down a side street, west down an alley (in some areas alleys are mapped as if they were nameless streets, an odd quirk in the data), south down another alley, and then west out to Cicero on a side street at an intersection with no light. I don't expect Google to know where every stop light is, but it shouldn't need to know that to avoid generating that route.
Another big issue for generating bike routes is data. Some data on urban bike routes actually exists. The city has a great map that has just about never steered me wrong. The Active Transportation Alliance publishes a print map of the whole area that covers pretty much all of the 'burbs -- its map also distinguishes between paved and non-paved trails, a vital distinction for road bikers. And the Illinois Department of Transportation has maps for download, which are very useful for finding which rural routes are paved and in good condition (or were at time of publishing). If they can get the rights where applicable and incorporate all this data they could generate great routes all over the state. As it is they mostly just have bike lanes and bike paths plotted. This means there's no useful information on the south side or the suburbs; it seems when there's no data Google's algorithm is much more likely to send you weaving on side streets, trying to turn left onto major streets from minor ones.
One type of data that will mostly have to come from users is on obstacles. Unusually difficult intersections, unusually bad pavement, bridges with open metal grating. The first route I tried to map had me cross under the BNSF tracks in Pilsen on Wood. The potholes under there are filled with water older than me.