Everyone I know in the AMS would like to make MR/MathSci free, but the problem is that it costs millions of dollars to produce and maintain (it requires a large staff in Ann Arbor and elsewhere, including many mathematicians), and no one has managed to find any other way to pay for it*. This is certainly something the mathematicians in the AMS are aware of and have thought about. The AMS attempts to make it as widely available as possible given the constraint that it has to be paid for. As far as I know, the revenue from MR/MathSci only pays to support it, not any of the AMS's other activities .[not so; see below.]
Posters don't seem to realize the huge effort that goes into maintaining a project like this (for example, every article has to be assigned to a reviewer, and every review has to edited). Certainly, I don't believe a free alternative would be able to come anywhere near the quality MathSci maintains, so my answer is no, a free alternative to MR/MathSci is not possible.
Perhaps free supplements to MathSci could be useful, but anything that drew potential reviewers away from MR/MathSci would harm, not help, what is an extremely valuable resource.
*Of course, the intelligent thing would be for the funding agencies in the wealthy countries (US,EU,Japan,...) to pay for MR/MathSci directly, so that it could be distributed freely, but getting them to do this seems to be hopeless.
Added: In response to Anton Petrunin's comment, here are some numbers. The AMS employs 15 mathematical editors (i.e., mathematicians) and a total staff of over 70 at Mathematical Reviews (in Ann Arbor). The total direct cost of producing MR/MathSci in 2008 was 6,569,000USD. However, contrary to what I thought, the AMS does use the revenue from MR/MathSci and its other publications to support a large part of its other activities (Member and professional services, general and administrative expenses). In 2008, about 24% of total publication revenue was used in this way. See 2008 report and ad.