The story...

Zinc discovered on metal samples at the WTC may (in combination with the presence of other chemicals) indicate the use of thermate.

Our take...

Professor Steven Jones explains that his tests on a metal sample revealed significant amounts of Zinc, and that this would be a likely thermite ingredient:

ZINC oxide would be a good choice to add to thermites: high-energy release. USGS independently confirms much Zinc in the WTC dust, 1500 ppm typical (up to about 3000 ppm)
http://pubs.usgs.gov/of/2001/ofr-01-0429/chem1/wtcchemfig4new11-7.gif
Source

In theory you might assume independent confirmation of the presence of Zinc is a good thing, but look at the quantities: 1500 to 3000 ppm? In other words, 0.15 to 0.3% of the WTC dust samples were zinc? Keep in mind the quantity of explosives Professor Jones says may have been required:

Phone interview with demolition expert, Brent Blanchard, 10 Feb 2006...

To bring down Southwark Towers, about 300 pounds of shaped charges (RDX) would be sufficient, he said.

(Then for a WTC Tower, about 1000 pounds of explosives would be sufficient. This would only require an estimated 10 men [foreigners?] to install the cutter charges, mostly in the central core/elevator shaft areas.)
http://worldtradecentertruth.com/JonesAnswersQuestionsWorldTradeCenter.pdf

Only 1,000 pounds of explosives in total. Professor Jones doesn’t spell it out, but any Zinc would surely make up only a small proportion of this. Even, say, 10% of the total, 100 pounds, surely couldn’t be enough to make up 0.15% of the WTC dust. It seems there must be additional sources. That’s what another survey says, too:

The legacy of the World Trade Center attack, Olsen and colleagues found, is recorded in New York Harbor sediments as a layer containing high concentrations of several elements, copper, zinc, calcium, strontium, and others. Results indicate that the deposition of World Trade Center ash, via fall-out from the atmosphere, urban runoff in streams or site remediation activities, could account for all of these elevated concentrations...

...Copper and zinc are also common components of building materials.
http://www.nsf.gov/od/lpa/news/03/pr0309.htm

Zinc is also related to construction in this analysis of WTC particles:

...particles between 10 and 53 µm had more construction-related elements (Al, Ca, Mg, Ti, Fe, Zn)...
http://pubs.acs.org/cen/NCW/8142aerosols.html

And what about those burning computers?

Amongst the hazardous components found in computers are zinc, cadmium, copper, chromium, mercury, manganese and arsenic.
http://worktwice.co.uk/rabbitt/computers.htm

Hazi looked at Pb, Cu, and Zn as indicators of combustion of WTC materials, such as computer parts, electrical systems, and office furniture.
http://pubs.acs.org/cen/NCW/8142aerosols.html

Whatever the zinc levels in WTC PCs, it seems to us that there is far more zinc reported than can possibly have come from “thermate charges”. And so there is no real basis for giving thermate a higher priority as a source than anything else, at least not until you’ve properly investigated what those other sources might be.