It is no secret that starting pitchers struggle in the first inning compared to the later innings of the ballgame. So far in 2013, starting pitchers have a 4.31 ERA in the first inning, with an opposing OPS of .742. In the second inning, the OPS drops to .720, with an ERA of 3.74. Part of this probably has something to do with quality of hitter, though so far this year spots 4-6 in the order have an OPS of .752, while 1-3 in the order has an OPS of .750.
So I looked at the all pitches thrown in the 1st inning of 2013, along with all the pitches thrown in the 2nd inning of 2013. I took out all the unknown pitch types. I also ignored things like pitchouts, intentional walks, and the FA tag (though these last three things weren't removed until after, so they still played in the percentages). I sorted the pitches by MLBAM pitch type and looked at their average locations and velocities, comparing all the pitches thrown in the two innings to see if there was a discernible difference.
Here is the first inning graph, showing where each individual pitch was located on average, regardless of platoon and handedness:
By contrast, the second inning:
The average vertical release point is the same in total from inning one to inning two, so there doesn't appear to be anything obvious going on with pitchers' deliveries, or at least how they end.
From the first inning to the second inning, there is a drop in four seam fastball usage of nearly four percent, and there is an increase in slider usage of two percent. Moving fastball usage drops about a percent, while sinker usage stays about the same and cutter usage is the same. Changeups see an increased usage of about a percent, while curveballs saw an increase of over a percent.
As far as average location difference goes, the 4-seam fastball is located better in the 2nd inning, as it is closer to the center of the strike zone slightly (meaning it is thrown to both sides of the plate more on average), and slightly higher. It isn't a dramatic change, but with the large sample size, any small change is pretty significant. The cutter is located a little lower on average, while the slider is about the same, and the curve is actually thrown a little higher on average. The moving fastball is similar to the 4-seamer, in that it is located closer to the center of the plate on average and a little higher.
Dickey, the only one to throw knuckleballs in the first two innings of a ballgame this season, improved from the first to the second just like league average. The knuckle is actually a tick softer in the 2nd inning, and he locates it more arm side on average (though it is slightly higher).
Hector Santiago is the only one that throws a screwball, and he locates it, on average in the first two innings, outside of the strike zone, and that is why it doesn't show up in the graphs. He is actually a lot better than in the first inning than the second inning. In the second inning, his screwball is actually lower on average and closer to the strike zone.
To me, it seems that the biggest difference is fastball usage and fastball location. The fastball is the pitch most pitchers throw the most, but it usually isn't as effective as off-speed pitches. For example, curveballs this year have a 10.8 % swinging strike rate, and changeups have a 14.8 % swinging strike rate, both of these rates much higher than fastballs, so it would make sense that pitchers would have more success by throwing the fastball a little less and more breaking balls if they can locate them (of course, fastball velocity is still very important, and there is a point of no return, but there is no correlation between fastball usage and overall success, as qualified pitchers have a -.097 between fastball percentage and FIP -).