I decided to do a little bit of orbit calculation; how many orbits around the Sun that Messenger has made and how many it will make. Using this trajectory page as a guide, I've come up with:

Earth 1, 2004 Aug 3 - 53220
Earth 2, 2005 Aug 2 - 53584
Venus 1, 2006 Oct 24 - 54032
Venus 2, 2007 Jun 5 - 54256
Mercury 1, 2008 Jan 14 - 54479
Mercury 2, 2008 Oct 6 - 54745
Mercury 3, 2009 Sep 29 - 55103
Mercury 4, 2011 Mar 18 - 55638

The first one is the launch of Messenger, and the last one is insertion into Mercury orbit; all the others are flybys.

The numbers at the end are Modified Julian Dates, which are easier to compare than typical calendar representations.

Earth 1 - Earth 2: 1 Msgr orbit
Earth 2 - Venus 1: 1 2/3 Msgr orbits
Venus 1 - Venus 2: 1 Msgr orbit, 1 Venus orbit
Venus 2 - Mercury 1: 1 1/2 Msgr orbits
Mercury 1 - Mercury 2: 2 Msgr orbits, 3 Mercury orbits
Mercury 2 - Mercury 3: 3 Msgr orbits, 4 Mercury orbits
Mercury 3 - Mercury 4: 5 Msgr orbits, 6 Mercury orbits

I will now consider what Messenger will be able to see in its upcoming flybys. This will be determined by how Mercury rotates.

Mercury's rotation period is rather odd: it is 2/3 Mercury years relative to the stars, and thus 2 Mercury years relative to the Sun. So a Mercury "day" is 2 Mercury years long.

Note: 1 Mercury year is about 88 Earth days.

Mercury had been visited once before, by the Mariner 10 spacecraft, which flew by three times. But between each pair of flybys was 1 spacecraft orbit and 2 Mercury orbits, and thus 1 Mercury day. This meant that Mariner 10 saw the same half of Mercury all three times, which I will call the Mariner hemisphere. The other half of Mercury's surface is thus the anti-Mariner hemisphere.

As reported in this news page, Messenger has seen half of the Mariner hemisphere and half of the anti-Mariner hemisphere. So on its next two flybys and on its arrival in Mercury orbit, Messenger will see the other half of both the Mariner and the anti-Mariner hemispheres. This is because there is an odd number of Mercury days from the first to the second flyby, but even numbers of Mercury days between the second flyby, the third flyby, and orbit insertion.

Messenger will then orbit Mercury for the next Earth year, which is about 2 Mercury days; it will see both the Mariner and the anti-Mariner hemispheres from the full range of solar illumination directions.