Here's how the Blockbuster computer system works:
There are national database computers that store all of your identification info, searchable only by your membership number (6-digit store code -- where you first got the card, your "home store") + (5-digit identifier -- for each each store). Note your mem. # is 11 digits.
When you first get a card, you fill out the form and they make you a card and put you in the computer. You will remain in THAT computer, at your 'home' store, for a while. Once you're in a computer, you can be searched by your last name.
Note that when you go to a Blockbuster OTHER than your 'home' store, you are basically required to have your card, otherwise they make you fill out a form and get a new one . . . and a new number. This is because they can look you up in the national database (oh yeah, I forgot to add -- this shows that the card they issue you is INDEED good for the entire US and Canada) (yes Canada!) by your unique 11-digit membership #, but NOT by your name.
Through all this you can begin to see that the computer systems at each Blockbuster are NOT --
NOT -- networked in any way! So any type of redemption card they give you . . . pretty much EVER -- including this one! . . . can be used independently at any Blockbuster at which you choose to use it. The key: don't look like you know what you're doing, maliciously

D) cruising around town screwing Blockbuster at every turn because they choose to cut costs and not network their archaic computer system.
ONE CAVEAT: This is important. Now that you know a bit more about the BB database, you must know that while it is easy to get away with this redemption card exploit, you CANNOT run away from late fees. Once you owe a Blockbuster money -- note that you do indeed owe that SINGULAR Blockbuster money; you do not owe "Blockbuster" (the company) money -- they will hound you, the fees will pile up, and if you take too long to pay them back, they WILL report you to other stores, and they will notify the corporate collections dept. Oh yeah, that penultimate item is worth noting: indiv. Blockbusters can put a "hold" on your acct. and send this to a national computer, which will send it to EACH and EVERY Blockbuster. But this is typically just when you have a late fee at another store, or they need updated info, or you're in Collections . . . like I said, if you can stay in the clear with each Blockbuster you visit, you'll be
just fine.
Rewards cards . . . I'm not so sure. I believe there is a little more at work there, and maybe your membership is more pervasive nationally . . . I don't know.
Have fun! Don't forget to Go Home Happy! (TM)