Those positive reviews for Microsoft’s (MSFT) new Windows Phone 7.5 operating system are raising a smile in Redmond, I’m sure.

But the big sigh of relief that you can hear is from Nokia (NOK). That company bet its smartphone future on Microsoft’s operating system when it decided to sideline its own Symbian operating system in favor of Microsoft’s platform.

The transition has been extremely painful for Nokia, as the company saw phone sales fall by 20% in the second quarter. Nokia, once the market-share leader, was passed by both Apple (AAPL) and Samsung (SSNLF).

Nokia hopes to begin slowing the fall in its global market share against iPhones and Android-based phones with new models expected to be announced at the yearly Nokia trade show in London at the end of October. (Assuming, of course, that Nokia can then get the new phones to market by early November to meet the holiday season.)

Nokia’s strategy looked very shaky after Microsoft announced its own attempt to get back in the phone game last year with Windows Phone 7. Reviews were generally positive, but questioned if the operating system was ready to play with the big boys.

Windows Phone 7 didn’t have Twitter support, Internet sharing, copy-and-paste, visual voicemail, or multitasking. All those competitive gaps have been filled in Windows Phone 7.5.

Plus, the operating system has a unique look and feel that makes it something other than an iPhone wannabe. The home screen displays color tiles that represent collections of information and applications organized around a theme. The People hub, for example, collects contacts and social network feeds. The tiles also include automatic updates with things like newly received e-mails or calendar changes.

I wouldn’t say that Windows Phone 7.5 marks the end of Nokia’s struggles. Getting system operators to put Windows phones on sale next to Apple and Android models is tough. And Microsoft badly misjudged its response to Apple’s iPhone, so it can’t be said to have much mindshare among consumers.

Nokia is also seeing intense competition from Asian phone makers at the lower end of its product offerings. That has eroded margins, as the company has cut prices to retain market share.

At the upper end of the market—in smartphones, where Nokia competes with Android and Apple—it’s likely that Nokia won’t be able to rebuild market share sufficiently to stabilize operating margins before 2013. For that time frame, the company needs another Windows Phone version beyond 7.5 to bring it to parity with the continuing improvements by competitors.

Credit Suisse projects that Nokia’s share of the smartphone market will go from 34% in 2010 to 14% in 2011, then to 8% in 2012, before creeping back up to 9% in 2013.

A gain to a 9% market share wouldn’t put smiles on the faces at Nokia…but given that many were writing the company off for dead, it would be a significant turnaround.

If Nokia can get some buzz at the London show and get new models to market in November, I think that this could be a $7 stock (ADR actually). That would represent a 14% gain from the $6.15 price on October 11, but it wouldn’t be a huge recovery considering that the shares traded at $11.75 on February 9.

I think that’s enough of a reward in the very short term to make this a reasonable near-term buy, if not a buy for the 12- to 18-month time horizon of Jubak’s Picks. But even as a short-term trade, I certainly wouldn’t chase the shares much above today’s price. (The company reports what is certain to be a bad quarter on October 20.)

Don’t get entranced by the current 9.3% dividend either. Nokia has historically paid the dividend just once a year—and the last payout was in May, so you’ll have to wait a while. And there’s a serious chance that the company will cut its dividend as it works its way through this tough transition.

Full disclosure: I don’t own shares of any of the companies mentioned in this post in my personal portfolio. The mutual fund I manage, Jubak Global Equity Fund, may or may not now own positions in any stock mentioned in this post. The fund did own shares of Nokia as of the end of June. For a full list of the stocks in the fund as of the end of June, see the fund’s portfolio here.