Not very many, although the show does seem to be getting into more of a "groove", so to speak, as it goes along. Pacing is more even and the new Shinki, Hina/Strarf (Minori Chihara), has a bit more depth than the others, so while it's still far from the best thing on TV, the show is certainly improving.
As with episode 1, the plot of episode 2 primarily concerns a simple household chore escalating into something ridiculous - in this case, an attempt at a home-cooked meal being sabotaged by two antagonistic, pun-spewing Shinki who turn the meal preparation into a big action scene, complete with a live octopus whose tentacles are utilized to their fullest fanservice potential. It's a silly bit of fluff, and I will readily admit to it - I actually got a few laughs out of it. Still not quite as funny as many other slice-of-life shows, but the action's well-done and if the humour keeps improving then we might just have something worthwhile here.
I mentioned above that Hina (or Strarf, as she insists everyone but her "Master" refer to her as) has more depth than the others, and while that's admittedly damning with faint praise, she is definitely more interesting than Arn, Lene or Aines. As a Busou Shinki, she feels it is wrong to not be used to fight as she was intended to, and has trouble fitting in with the strictly domestic routine that the others adhere to so enthusiastically. Robot angst might not be anyone's cup of tea - sure isn't mine - but she shows that the writers are at least trying to create a character you might have a reason to care about.
Episode 2 finds the show steadily improving in every aspect, but the fact of the matter is that it still is a show that reeks of its own irrelevance. As a reader pointed out in a comment on the previous review, many of the Shinki featured in the show are based on rare, out-of-print models, so the show is essentially a promo for products that one can't buy. It's sometimes amusing and the animation conveys action well, but it is hard to truly recommend a show like Busou Shinki when shows such as GIRLS und PANZER offer the same blend of action and comedy with more finesse. Maybe further episodes will improve and change this, but for now it seems doomed to be just one of the many forgettable anime that come out every season.