(Abridged) This paper reports new Very Large Array (VLA) and Very Long Baseline Array (VLBA) observations of the extragalactic source B1849+005 at frequencies between 0.33 and 15 GHz and the re-analysis of archival VLA observations at 0.33, 1.5, and 4.9 GHz. The structure of this source is complex but interstellar scattering dominates the structure of the central component at least to 15 GHz. An analysis of the phase structure functions of the interferometric visibilities shows the density fluctuations along this line of sight to be anisotropic (axial ratio = 1.3) with a frequency-independent position angle, and having an inner scale of roughly a few hundred kilometers. The anisotropies occur on length scales of order 10^{15} cm (D/5 kpc), which within the context of certain magnetohydrodynamic turbulence theories indicates the length scale on which the kinetic and magnetic energy densities are comparable. A conservative upper limit on the velocity of the scattering material is 1800 km/s. In the 0.33 GHz field of view, there are a number of other sources that might also be heavily scattered. Both B1849+005 and PSR B1849+00 are highly scattered, and they are separated by only 13'. If the lines of sight are affected by the same ``clump'' of scattering material, it must be at least 2.3 kpc distant. However, a detailed attempt to account for the scattering observables toward these sources does not produce a self-consistent set of parameters for such a clump. A clump of Hαemission, possibly associated with the H II region G33.418-0.004, lies between these two lines of sight, but it seems unable to account for all of the required excess scattering.

23 pages, LaTeX2e AASTeX, 13 figures in 14 PostScript files, accepted for publication in ApJ