Gaming the Help System
1. Follow the Leader/AKA the Gandalf Effect
Take the person with the highest stat, have them deal with the higher obstacle things, have the rest of the group each throw in Helping dice in order to get the advancements. The leader often will get nothing beyond a Routine test at best, but everyone else gets a good advancement out of it.
2. The Leapfrog game
Let's say you have two characters close or identical in a stat. One will take the test, using as many ways to get extra dice as possible - Linked Test, FORKs, Working Carefully, etc. etc. The other one puts in a Help die. Notice that the Helper isn't penalized for all these extra dice - as long as it passes, it counts as if they met that Ob with their given stat.
Next time, switch roles.
3. Someone needs my Help!
Find an NPC who is has the higher stat, is doing tough Obstacles, and offer your Help. This is easiest to do with Resources, since nearly no one turns down financial assistance. Perception is harder, by it's nature. Faith is the hardest to find someone, but of course, if they share the same Faith as you, they'll probably be happy to take on a disciple and then the tests should come easy.
Practice
Obviously, not easy to do during an adventure, but between adventures, or while waiting for someone to heal up, it's a great time. In general, if you're not doing anything particularly useful, it's always a good time to ask the GM if you can get practice. "Hey, we're going to be riding on horses for weeks at a time. Can I get part of that as Forte practice and part as 'Horse-wise'?"
For things like Perception or Faith, it's a little tougher but not impossible, you just have to be creative or at least have an NPC who can tell you how to practice them.
Artha, the gambling way
You can always spend Artha. If you have it. The thing to remember is the more dice you're rolling, the more likely you are to get a benefit from open-ending a roll. That said... Artha doesn't come quick enough to really pull one of these kinds of tests more than once every 2-3 sessions at best.
Greed, the one exception
Spend a persona point, add your Greed to a test involving the things you have Greed over - the dice count as Artha dice, so you can start making big rolls without having those dice count against you. It's pretty easy to see how this can work for Resources rolls, a bit harder for Perception, and unfortunately, Dwarves don't get Faith at all.
Eleven Grief takes a full Deeds point, which makes it too rare to be that useful, and while Orcs can roll Hate in place of other skills or stats, the advancement only counts towards Hate.
The Fact is...
Practice and Help are the ways to go. Remember Burning Wheel also is built on the assumption of the long term, old school campaign length - it may take dozens upon dozens of sessions to advance these things. You should probably assume that unless you have a game group like that, that a lot of these stats will stay static for the entire campaign.
Resources: Easy to find situations, easy to Help, can't practice.
Perception: moderate to find situations, moderate to Help, can practice.
Faith: moderate to find situations, hard to Help (that is, hard to find other people with Faith), can practice.
What is the purpose of not allowing tests for advancement to be converted to less difficult tests, and what would change if I removed this rule?
Burning Wheel's general design philosophy is built on tugging the protagonists between heroic action and realistic vulnerability.
The requirement for tough tests pushes players to either seek out difficult challenges OR push on while injured or otherwise at a high disadvantage - very heroic. The requirement for routine tests pushes players to seek out maximum advantage in dice vs. obstacle, or, to take advantage of teachers or practice.
Typically in play, a player will find a skill/stat getting used more for either very difficult situations or very routine situations. If it's the former, they now have to seek out or engineer situations where they are at an advantage to get the skill/stat to raise. If it's the latter, they need to throw themselves into difficult situations.
In both cases, it pushes players to think dramatically and never take a single approach to the game or the world.
Here's another part of the rules that ties into it that a lot of people miss early on: between FORKs, Linked Tests, Advantage Dice, and Help, a group of PCs working together can easily throw an extra +2D to +5D on many rolls (if their skills are high and they're Helping/FORKing, that can go even higher...)
Getting those Routine tests isn't as hard as you might think, but it does require working as a group (or, rallying up enough NPCs to help you out...) It forces the players to also draw upon other characters and interact socially more, as well.
Best Answer
You can see for yourself the changes to the "Hub and Spokes" rules, as they are the first 90 pages, and are included in the preview at http://www.burningwheel.org/?p=276. Under the word "Here" in the fourth paragraph on that page is the download link for that preview.
Luke has mentioned that there are numerous small changes to Fight, specifically the processes for range setting, Duel of Wits, and Range and Cover.
Sorcery no longer adds will dice to rolls to cast, reducing the difficulty of advancing Sorcery as one no longer needs insane Obs to get Difficult and Challenging expenses.
Perception is no longer open ended.
Let it Ride drops the bit about referees cheating.
A significant change in terminology: "Graduated Test" replaces the older "Open Test", avoiding the frequent confusion between open ended rolls and open tests.
Some minor changes to the difficulty/test type table at the low end.
Many lifepaths have been revised.
I've not yet gotten BWG yet, only the preview, so I can't be much more detailed, but I'll note that the hub and spokes text is not readily different at first glance, but some small changes are present.
References
http://www.burningwheel.org/forum/showthread.php?11076-Burning-Wheel-Gold-Errors-and-Changes