Risks/problems of a short chain I've put a new chain on my bike using method 3 from Zinn's art of road bike maintenance to determine length:


  "Wrap the chain around the big chainring and biggest cog without going
  through either dérailleur. Bring the two ends together until the ends
  overlap; one full link (Fig. 4.7) should be the amount of overlap
  (Fig. 4.10)..."


However, I didn't notice that my fingers must have slipped at some point because I remeasured the size after breaking the surplus pieces off &amp; the overlap was gone (facepalmed myself with a greasy hand at this point). 

How big of an issue is this likely to be? What are the problems associated with an overshortened chain? Realistically, should I be running down to the bike shop and buying a second chain in as many days (whilst trying to pretend I hadn't)?

I rarely (if ever, I dislike cross-chaining) end up on both the big cogs and chainring at the same time therefore the chain &amp; rear dérailleur would rarely be under maximum possible tension. I'm aware it's not a good idea to re-add links and given I'm about to head to the Alps I don't want a weak chain!
To quote Sheldon Brown: "If the chain is too short, it will be at risk for jamming and possibly ruining the rear derailer if you accidentally shift into the large-large combination. Never run with a chain that is too short, except in an emergency." (I will say that depending on if your chain is short enough, it can happen in combos other than large-large.) 

Here is a good article on sizing chains. 

If its a new chain, I wouldn't hesitate in breaking the chain at a different link and adding some of the extra links back to it. But you really should get the chain to be of the right length before riding. 

Also, for what its worth, the easiest way to size a new chain for a bike which hasn't had a cassette/chainring size change occur is to start with the old (properly sized) chain, and use that to size out the new chain. Much less annoying than sizing the chain from scratch.