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We report on the analysis of 436.1 hrs of nearly continuous high-speed photometry on the pulsating DB white dwarf GD358 acquired with the Whole Earth Telescope (WET) during the 2006 international observing run, designated XCOV25. The Fourier transform (FT) of the light curve contains power between 1000 to 4000 microHz, with the dominant peak at 1234 microHz. We find 27 independent frequencies distributed in 10 modes, as well as numerous combination frequencies. Our discussion focuses on a new asteroseismological analysis of GD358, incorporating the 2006 data set and drawing on 24 years of archival observations. Our results reveal that, while the general frequency locations of the identified modes are consistent throughout the years, the multiplet structure is complex and cannot be interpreted simply as l=1 modes in the limit of slow rotation. The high k multiplets exhibit significant variability in structure, amplitude and frequency. Any identification of the m components for the high k multiplets is highly suspect. The k=9 and 8 modes typically do show triplet structure more consistent with theoretical expectations. The frequencies and amplitudes exhibit some variability, but much less than the high k modes. Analysis of the k=9 and 8 multiplet splittings from 1990 to 2008 reveal a long-term change in multiplet splittings coinciding with the 1996 "sforzando" event, where GD358 dramatically altered its pulsation characteristics on a timescale of hours. We explore potential implications, including the possible connections between convection and/or magnetic fields and pulsations. We suggest future investigations, including theoretical investigations of the relationship between magnetic fields, pulsation, growth rates, and convection., 18 pages, 20 figures, 5 tables, accepted for publication in the Astrophysical Journal