"various doubts" is correct and usable in written English.
You can use it to refer to multiple questions or uncertainties about a certain topic. For example: "I have various doubts about whether this is the right choice for me."
"We do have various doubts about what Iran is doing," Mr. Medvedev said last week.
Now I like Jon Huntsman, my various doubts about his campaign strategy notwithstanding, and I wouldn't mind seeing his candidacy gain a little more traction.
They both want the same thing, but the former is hopelessly outclassed by the latter, and must move to a position of grateful dependence, despite nursing various doubts about the vigilante's methods.
Science 303: 1669-1674) The investigation on the 2004 Science paper in which the establishment of the first human ES cell line from cloned blastocyst was reported was initiated in response to various doubts raised on photographs of the cells and results from DNA fingerprinting analyses.
With regard to the text-work distinction and the more general arguments given in support of it, various doubts have been raised.
Kant's question, then, is how we might defend reason from various doubts and worries[14] and how we might discipline it without begging questions (for instance, by invoking claims or premises that themselves are open to doubt) (cf. O'Neill 1989: Ch. 1, 1992, & 2004).
Like solo travellers, couples have various travel planning doubts and logistics to negotiate.
The collective hopes that its various worries and doubts about the government's ability to adequately monitor the mining sector will prompt the World Bank's Inspection Panel to investigate violations of policy in the shaping of the bill.
There is one matter that is beyond all doubt: various members of the US military and the UK intelligence services will start briefing against Aamer.
Expect it soon, the FCC is poring over it and objecting to various bits, no doubt.
The band's merchandise and various ephemera no doubt find themselves housed in many a broken home and trailer park, alongside plenty of empty bottles of Faygo and hopelessly scratched, unplayable, PS2 discs.
