I could be on the wrong track here, but there might be another culprit:

Are there - by any chance - any glissandi in the document?

No. It happens on every document.

>The experts at Finale say that my midi keyboard has a wheel that alters the pitch and that is the problem.  However just about any keyboard you buy has that wheel.<

I'm not buying it either. You're right that nearly all MIDI keyboards have a pitch bend wheel but most, like mine, are on a center detent. If your controller also has a modulation wheel, that is not on a center and can cause problems unless kept in the Off position. 

This is not a common complaint. What happens when you disconnect your MIDI controller playback through AU or VST instruments?

I know my (ancient) DX7 has a slider and function setting that allows it to shift the pitch of the entire instrument on a "long-term" basis (quite separate from the Pitch-Bend wheel). This function is useful when transcribing off a recording that is not in A 440, but once I inadvertently hit he function button and moved a binder on top of my DX7 and suddenly the pitch was wildly off. So MM's suggestion (even if badly expressed) may have had validity for certain situations on certain MIDI keyboards.

Same. The point is Finale goes out of tune. Starts ok, but after a while certain instruments play back at wrong pitch. The only thing I have found is to stop playback, reload instruments, and start again. Hardly the performance one expects of a decent application.

I have found a solution to this problem.  I'm convinced it lies in a bug regarding the pitch wheels.

There is an option on my midi keyboard (E-MU 49) to Bypass Knobs.  This is under a section called Function Buttons.  I selected this option (Knob Bypass,) and I haven't had any further problems.

-JT

Well, see my comment just above.  I thought the problem was over, but it isn't.

If any of you Finale people are reading this, I would really appreciate your answer as to why this is happening.  Obviously, it's not only me, and this is a massively annoying problem.

John,

Although Finale people MAY be monitoring the forum, and sometimes even answer, they won't take OFFICIAL notice until you open a support ticket. Use the Submit a Request tab at the top of the page.

Thanks, Mike.  I just filled out the proper parerwork.  We'll see, I guess.

My experience: Finale 2012--inexplicably and suddenly playing everything in the top staff out of tune (tried in multiple files). On a hunch, I set my mod wheel on my MIDI keyboard to center...and that fixed everything. My mod wheel has *never* changed the pitch of playback from Finale, nor should it. The only thing that has changed on my system is this: I downloaded a new synth VST that can import scala files...could be the culprit? So weird.

>The only thing that has changed on my system is this: I downloaded a new synth VST that can import scala files...could be the culprit? So weird<

Not weird at all. There are many threads on this including this from a couple days ago — follow the ARIA manual and other links:

https://makemusic.zendesk.com/hc/en-us/community/posts/1500000719001-playback-at-430-and-not-440 

You can also enter Scala into the search box above to find more threads on the subject.