The layman looks at the exchange rate of the dollar as a bearing on the strength of the U.S. economy, and I've anecdotally seen it take on a national-pride role. In more complicated terms, a weakening dollar can either mean changing inflation expectations (toward higher inflation), an exodus from dollar denominated securities and/or U.S. debt, or simply more dollars entering circulation (i.e. "actual" inflation).
When the dollar starts to falter, dollar holders, but especially foreign dollar holders, start to get concerned. Take for example China. A large chunk of their sovereign wealth is denominated in dollars. This works for trade reasons (they do a lot of trade with the United States) and to help ensure confidence in the Yuan, which is unofficially pegged to the dollar. But it has led to public concern on the part of China (specifically PM Wen Jiabao) as to the security of their investments.
On the plus side, when the dollar is weak, exports and manufacturing get a boost. For example, the market moving story today was the Institute for Supply Management’s factory index rising to 55.9 where above 50 indicates expansion (this is the highest the index has been since 2006). After having done research on steel companies, Goldman Sach's conviction buy rating for U.S. Steel Corp. was partially because of a weak dollar environment.
After the market's positive reaction to the manufacturing report, and Bernanke's previous concern that unemployment might erode a U.S. recovery, I would not be surprised if the Fed put dollar strength on the back burner except in extreme cases, in favor of promoting job creation and strength in the manufacturing sector. In light of the U.S.'s forays into car companies (read: Chrysler and GM), a weak dollar climate might be great for taxpayers, too. Because of this, I see the positive manufacturing report as a signal of more to come rather than a one time event (in terms of monetary policy implications).