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"We recently presented at a tradeshow, and we had an email opt-in form/kiosk at our booth. We want to send them a thank you note, plus some followup information."

Okay to use. So long as each attendee/visitor knew they were going to be receiving emails from your company, you may use Lead Liaison. We recommend setting up a new list for these recipients, and sending a "hey, thanks for visiting us at the so-and-so show" email. Ask them to subscribe to your regular email, or let them know you'll be sending them regular newsletters soon, and provide a link to opt-out. Send this email as soon as possible after the show. It's better for sales, and it'll prevent the "who the heck are you" effect from waiting too long to send.

"I own a restaurant, and we leave a little card at every table, asking people to subscribe to our newsletter"

Great, feel free to use Lead Liaison. Be sure to contact people fairly regularly, because permission goes stale in 6 months. People will forget you and report you for spamming if you wait too long. Then, it's difficult to prove you have opt-in permission, should an ISP threaten to blacklist you. Save a copy of those little opt-in cards you used.

"When people buy from my online storeus, I we ask them if they'd also like to subscribe for email newsletters and promotions"

They checked a box to subscribe to emails? Sounds like they gave you permission, and they'd like to hear from you.