Now... Pottermore is an interesting site because it's not only effectively a miniature social network for fans, but a little gaming hub, and this can definitely be seen in the Sony-affiliated games that Pottermore has put out, like the version of Pottermore for the PS3, and the Book of Spells. However, this has an interesting little progression on the site itself.
In the beginning of beta, that is the interesting part, and I honestly don't have much to present, as a function of Pottermore wasn't present when I was first there. This would be the dueling system, though I recall rumors that it randomized spell potency for different people (As in Bob could get a 142 on an Incendio while Jamie was maxed out at 44, but Jamie could get a 142 on a tongue tying hex and bob couldn't). This was coupled with a system that allegedly allowed wand growth, so at first your duels would be low scoring, but improve as time went on, with different growth rates and caps for different wands. Needless to say this has an idea of realism when thought about, and even more importantly, it makes you want to play more, and duel more so you can keep growing. However, this proto-dueling is far from what we got in the end. Effectively, as it was after this point, it was a rhythm game. Each spell had its own rhythm and different max potencies. Again, this made some sense, and more importantly, it eliminated a "seniority" gap that would be inevitable. While dueling was taken down some time in the first few days, when it re-premiered in November, it was a massive hit, and allowed multiple players to storm the leaderboards. This is what keeps dueling as the most important way of earning points on Pottermore to date. However, the lack of growth in this version, and the lack of randomization have effectively crippled some of the motivations to keep dueling, especially if one were bad at it. There were attempts to fix this when dueling was adjusted to make it compatible with HTML 5, but the removal of Flash components made dueling far less stable, and more confusing to experienced players. Some have managed to do better under this system, but it makes it harder to work through unless someone watches the rings very carefully, and has sufficient hardware and internet.
As for potions, this is an interesting note, as potions all used to be 5 points, with 1 point for a regular failed attempt, but -5 for a catastrophic failure (only done by overheating). This actually combined with very slow brewing times to motivate people to choose short, cheap, easy potions (like cure for boils), while avoiding the longer potions that could take upwards of 3 hours to finish. In addition, some individuals would earn points quickly via failures, which would eat the ingredients, but give points faster, though this was fixed before beta ended. Midway through beta, both the point value and times for each potion were changed. Though it was only upon the release of Chamber of Secrets that new potions and galleons were given out. Now, potioneering has the downside for being a limited way of making points (costing at minimum 15 galleons). Meaning that any galleons earned will limit the amount of potions you can potentially make, though this has been fixed as many ingredients can be found and recollected when the amount runs out. This makes it so individuals can make up to 336 points a day purely through potions (while dueling can make upwards of 1,000, with a known maximum of around 10,000 pre HTML 5 change). Potions has also been remade to work on tablets due to HTML 5 capabilities, and this works in its favor as this means potions can be made on phones (though the small size provides some difficulty unless styluses can be used).
There are indeed other games on pottermore, but these are miniature events, and the only one with some popularity past its reveal was the gnome tossing, again revealed in Book 2. Hopefully Pottermore will help and produce a new game for us to enjoy, with some theories due to hidden bits in the coding being Wizard's Chess. Though other speculated ones would be Gobstones, Herbology, and the events in Book 4. Other speculation is that Pottermore will not add any more games, though there will be eventual expansions onto the dueling and potions sections, with dueling remaining unchanged in it's basic format since Book 1 (though Book 3 made it HTML 5 comparable), and Book 2 released 3* new potions, including 2 potions that are effectively useless for all those in slytherin. This also makes it so the potions have a maximum return of roughly 3 points for roughly a day's work of brewing.
Now for my thoughts.... both of these were fun at first, but over time they've definitely become stale. While dueling was challenging when most individuals were moderately decent at it, the change fixed that and made it MORE challenging, though less rewarding for the challenge. In addition, potions are the slower and less glamorous thing, even within the books, though the amount of points awarded for completing potions should reflect better on the time investment, with rewards for both the initial step and the end step, as well as a general boost in the points awarded. Dueling on the other hand, I would love to see it begin to resemble the proto-duel once again, as well as divide individuals into different "classes" so they face like challengers. This would give a reason to relax while dueling, and a reason to duel constantly to "rank up". In addition to certain spells that may only be accessible by advanced ranks, this would be more complex, but give users a better investment into visiting Pottermore daily.
*(Technically 3 new potions, though there was a phase 1 Polyjuice and a phase 2, and they are treated by Pottermore as separate potions, with phase 1 being a pre-requisite in order to brew phase 2.)