We have mapped [O I] 63-mu-m and [Si II] 35-mu-m fine-structure line emission in M17SW using the cooled grating spectrometer aboard NASA's Kuiper Airborne Observatory. In addition, we have measured the intensities of the [O I] 63 and 146-mu-m, [Si II] 35-mu-m, and [C ii] 158-mu-m at four positions. We have also made a strip scan of the [O I] 63-mu-m line intensity across the ionization front. Finally, we present new 50 and 100-mu-m continuum maps of the M17SW cloud at comparable resolution (30"-40") to the far-infrared line observations. The [O I] 63-mu-m and [Si-II] emission defines a thin (approximately 80", 0.85 pc) ridge which separates the ionized gas surrounding the luminous 0 stars in the northeast from the dense molecular core to the southwest. These observations demonstrate that the [Si II] arises from the photodissociation region (PDR) rather than the H II region. The [O I] map shows two distinct peaks along the ridge, which both border warm molecular clumps. The [Si II] map shows only one peak, which falls between the two [O I] peaks. The [Si II]/[O I] ratio varies somewhat over the mapped area, but is of order unity, considerably larger than predicted by the standard models. We have analyzed these new data together with earlier observations of molecular and ionized gas in this region. Assuming a homogeneous density distribution, numerical modeling yields densities and temperatures of approximately 3 x 1O(4) cm-3 and 300 K for the atomic zone. However, the homogeneous models cannot reproduce the observed spatial distributions, absolute intensities, and line ratios. Hence, we present a three-component model for the M17SW PDR consisting of clumps of density 5 x 10(5) cm-3 embedded in an interclump medium of density 3 x 10(3) cm-3. This clumpy core is surrounded by a halo with density 300 cm-3. This latter model agrees well with most of the observed spatial distributions and peak intensities of the far-infrared and submillimeter emission lines. In particular, the observed high [Si II]/[O I] 63-mu-m ratio is probably a result of the larger column density of clumps in an edge-on geometry in combination with self-absorption in the [O I] 63-mu-m by the interclump medium. We find that the [O I], [Si II], and high-J CO emission emanates solely from the clumps, while the [C II], [C I], and low-J CO emission arises primarily in the interclump gas. The halo is necessary to produce the very extended [C II] and [C I]. In conclusion, we stress that the M17SW PDR encompasses a wide range of physical conditions and that the individual cooling lines emanate from the regions where their excitation conditions are best met.