Democrats want to use the federal government's no-fly list, meant to keep suspected terrorists grounded, as a guideline for enforcing new laws to restrict firearm purchases.

Senate Republicans blocked that effort last week, but President Barack Obama kept up his push this weekend.

"Right now, people on the no-fly list can walk into a store and buy a gun," Obama said in his weekly radio address. "That is insane." He made a similar appeal during his address to the nation on Sunday night.

The new initiative is reviving questions about the legality and efficacy of the no-fly list, which has drawn criticism and challenges in court by civil rights groups, including the ACLU.

After losing a key ruling in a recent lawsuit, the federal government in April said it would begin to proactively inform people of their status and create a more transparent system for contesting the designation — a process the ACLU once described as a "Kafkaesque bureaucracy."

While the criteria for adding individuals to the list remains murky , one thing is for sure: it's still a lot easier to get on the list than get off it. Even in clear cases of mistaken identity or clerical blundering, a name can linger in the system for years.

Here are a few of the most high-profile flying foul-ups (some of which are directly tied to the no-fly list, while others are less clear).

Cat on a leash

In 2004, a Washington-bound United Airlines flight from London was diverted to Maine after officials discovered Yusuf Islam, the singer formerly known as Cat Stevens, was on board. Islam was denied entry into the U.S. and made to return to the U.K.

"Celebrity or unknown, our job is to act on information that others have given us," Homeland Security Secretary Tom Ridge said at the time. "And in this instance, there was some relationship between the name and the terrorists' activity with this individual's name being on that no-fly list, and appropriate action was taken."

But there was no further formal explanation and Islam was allowed in 2006 to enter the U.S. without incident.

A famous senator

Sen. Ted Kennedy told the Senate Judiciary Committee in 2004 that he had been stopped and interrogated on at least five occasions as he attempted to board flights at several different airports. A Bush administration official explained to the Washington Post that Kennedy had been held up because the name "T. Kennedy" had become a popular pseudonym among terror suspects.

John Lewis's long year

On the same day Kennedy revealed his flight troubles, civil rights icon and longtime Rep. John Lewis revealed he, too, had been snarled by the watchlist dragnet. According to his office, the Georgia Democrat had over the course of a year been held up 35 to 40 times. Despite reaching out to a number of federal agencies over that period, Lewis' name had remained on a list.

Oh, baby

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No-fly headaches aren't just for international pop stars and federal lawmakers. In 2012, Jet Blue removed an 18-month-old child from a flight before takeoff.

The girl's mother, speaking to a CNN affiliate, said she was informed by an airline employee, "Your daughter was flagged as no fly."

The TSA, which usually remains mum on these matters, categorically denied that young Riyanna had been flagged. JetBlue later apologized, blaming the incident on a computer "glitch." There are multiple reports of children, at least two under the age of 10, being delayed because of similar errors.

The adventures of Ozzie and Harriet's son

The post-9/11 skies have not been so friendly to an assortment of David Nelsons, most notably the late actor and producer who starred as child on ABC's "The Adventures of Ozzie and Harriet." In 2002, a ticket agent in Los Angeles stopped him from boarding a Salt Lake City-bound flight after his name popped up on a watch list. He was eventually allowed to board, but many others with similar names were not so lucky.

Caught up in the story

Two journalists, CNN's own Drew Griffin and Stephen Hayes of the Weekly Standard, have also been tangled up in the messy system. Hayes learned he had been added to a terror database. Why? Hayes told NPR last year he doesn't know for sure, but says a TSA agent told him trips to Turkey, including a one-way flight into Istanbul, probably did the trick.