A:

Like any investment, wine can fluctuate in perceived value in the marketplace.  As for drinking it, by all means, it would be worth opening one evening with some friends as such an old Port is a rare treat.  If the wine has been well cellared it could be very pleasant, though of course it will be very different from a young to mature port - expect something with a character more like a very old and elegant Tawny at this point, and plan to decant it just 30 minutes before enjoying.  A few resources:  on this site, look at our Enjoying Port articles about The Lifecycle of Vintage Port in Bottle and Decanting Vintage Port, especially Charles Symington's notes about serving wines older than 40 years of age.

About the 1934 Vintage season:  the IVDP (the governing body for the Port trade) summarises the year as follows:  Exceptional quality, mature and fruity, despite being a year of unstable weather. Dry winter, rainy spring. Late blooming and fructification. A very hot July. Some rain in September. 

The guest books from our own Quinta do Bomfim have this note written during the 1934 Harvest: 

The Vintage started on September 24th. Except for one day of rain its been perfect vintage weather and fairly warm most days. The grapes have all come in looking fresh and very healthy and in fact seemed in perfect condition though the grapes were small. It should prove good wine as there was an absolute absence of disease of any sort or kind up to the very last.

Unfortunately Paul, Dominic, Rupert and Johnny are all travelling right now, and Charles of course is in the vineyards preparing for this year's harvest, so I have not been able to get any family tasting notes for you.  For quite recent tasting notes from some Port devotées, follow these links to  The Port Forum and For The Love of Port.  Enjoy!