Some of the drivers are nominated by their verbally abusive spouses. The hosts will point out to them how much of a detriment they are to their driving spouses, and they actually turn around their own behaviors. Sometimes, the epiphany is a Tear Jerker: one verbally abusive spouse (considered the worst they'd had on the show) went on a drive with the host with his own verbal abuse being played back at him during the drive. The man was absolutely crushed to realize how bad he was and made a conscious effort to change. His wife's driving performance (to say nothing of their relationship) improved drastically.
Jillian in Season 11. While her driving didn't necessarily improve, her relationship with her fiance improved drastically, with Andrew even pointing out, "Jillian might not seem like a whole new person to you, but that's because you only see her in the car," and her fiance confirming the improvement in their relationship.
Really, any time a driver graduates looking like he or she has become a good driver - not just "less bad than when they arrived" or "the least bad of those remaining".
The show really caring for Angelina's mental health, as evidenced by Dr. Kiru's request to turn off the cameras in Ever, and the offer for Angelina to obtain the necessary treatment away from the show. The show even took time to advertise a Mental Health institution saying that staying in silence is no way to help those who need it. Andrew's compassion and concern towards Angelina and Christine in their final episode also qualifies, especially given that he is the one to drive them back to the drivers rehab centre, as opposed to Christine doing so.
Brad of Season 6, not only improving his driving and becoming the final graduate, but also his wife Donna learning that she was part of the problem and changing her ways, resulting in not only him being a better driver but them being stronger as a pair. Donna apologized to Brad, and when he was announced to be the final graduate, she cheered and said "He worked hard for this!"
Aaron's graduation in Season 7. He consistently refused to graduate because he wanted to get everything he could out of rehab and he wanted to be a warning to the rest of the contestants. He was therefore the last graduate of the season. You can't help but smile when he does his final challenge (a drive on public roads) and performs almost perfectly (after accidentally running a stop sign); he is grinning from ear to ear and Andrew is quite relaxed.
Diane from Season 8 is shown to be lovey-dovey with her nominator/husband Stephane in her introduction bio clip, but it's even more Heartwarming when she greets him after passing her final drive with flying colors.
In Worst Driver Ever (S9), a couple of drivers actually graduate early on, including Chris, the original "winner" from Season 1, having actually spent time after the show training, studying and learning.
When the show got wind that George (S10) was scared that he was passing on his bad habits to his son, the show proceeded to bring his son to rehab and give him some driving lessons with Tim, unbeknownst to George. Later on, George is actually taken for a drive by his own son to show him that his fears are for nothing.
Later on in Season 10, when Mariah graduates, they proceed to bring in her tattoo artist so that Mariah can get a tattoo stating that she'll never drink and drive again.
Season 12 has Jana (Mike's nominator) getting a surprise lesson from Philippe in how to drive manual. 
During Season 3, Scott (the driving instructor at the time) makes a comment about how driving is like riding a bike. Shelby then openly admits that he's never ridden a bike before in his life. So what does Andrew (and the show) do? Well, they teach him how to ride a bike of course! You can tell that both Andrew and Shelby have a LOT of fun doing this.
Mike's graduation in Season 12 is this considering he had to relearn everything from scratch after a terrible car accident years ago. He wanted to stay longer, but the experts decided he has already improved enough.
In the finale of Season 12 Krystal was laughing and heckling Daniella when she was trying to complete a challenge. It offended Tyler so much he forced her to change spots so he could give Daniella more support. In fact, once Krystal got to her run, everyone refused to watch her run from the sidelines in support of Daniella.
In a bonus video, Tyler gave Daniella one of Andrew's shirts that he received after his near perfect mega challenge, and she in turn gave him the rear bumper of the Mustang that fell of during her run. It's nice to see these two respect each other despite both having rocky starts this season .
The day after the finale of season 12 aired, Daniella posted that she got a full "G" license.
After Season 12 aired, Krystal was interviewed on an Edmonton AM radio show, and she not only admitted that she was a terrible and reckless driver on the show, but also revealed that she had been getting help for her mental illness, and "would swear on my life that I have not touched my phone since October in a car". In a total 180 from her attitude on the show, she said she was grateful for the education she received on the show, tearfully apologized to all of Edmonton for her reckless driving, and explicitly told anyone who was on their phone while driving to get off their phone. For being one of the show's most infamous Scrappies, she has certainly come a long way.