The idea of treasure in 4e is simple: the DM has a list of stuff and money that you should get that level.
The consequence of this idea is non-trivial, as it leads to quantum treasure. If you carefully loot all of the random "trash" from monsters, pry out the iron nails of the doors, and otherwise find enough stuff to load up a cart and haul it back to town: you'll get the value of x treasure parcels, depending on how generous the DM is feeling.
If you fail to loot bodies for "trash" items and only carefully take obvious magic items and other "treasure" ... you'll end up with the same amount of gold at the end of the level *. In the Gygaxian sense, encumberance is just there to threaten the players with if they are hauling around ovbiously too much stuff without appropriate hauling mechanisms.
From Carrying, Lifting and Dragging:
Adventurers carry a lot of gear. When that quantity becomes extreme, it might be enough to slow you
down and otherwise hamper your capabilities. The amount you carry should rarely be an issue, and you don’t need to calculate the weight your character is hauling around unless it’s likely to matter.
To figure out how much of the dungeon furnishings you can carry around before taking penalties, use (as stated in the above link) strength * 10 in pounds. (A completely unrealistic number, BTW). exceeding that will slow you down by some amount. You can barely lift strength * 20 pounds, but then you're moving at best 2 squares per move action (you have the slowed condition.)
Looting, therefore, should only be done if the players actively enjoy counting rivets. (I sometimes actually do, though it tends not to be in games like 4e). At first level, grabbing items off of fallen enemies is actually kind of neat, though it very quickly becomes irrelevant when you have your own, magic, items. If a player wants to obsessively loot, let him or her, ask them to describe how they're storing the stuff not on their person, and treat it like a treasure parcel that has to be redeemed at the local blacksmith.
If the person wants "full value" for the iron bands, rivets, broken doors, and daggers that they collect, they are welcome to sell them at 20% to anyone who wants to buy, and have that value deducted from a future treasure parcel.
If you're interested in other treasure-abstractions, take a look at Penniless but not powerless 1 and penniless but not powerless 2 which explore a further level of abstraction (quite welcome, IMO) for 4e.
What your group should do is ask the DM, in advance, for the kind of awesome treasure that they want. The idea of wishlists is quite handy for the players and the DM and saves time all around. Then just don't think about the coincidence of finding the exact magic item you asked for, it breaks suspension of disbelief. :)
*This statement is less true for redbox, as treasure is randomly determined, but the idea remains the same, as the GM should treat the "load of trash" as a plot coupon for a treasure parcel. Quantum-treasure works, so long as you don't think of it like a simulation.
I hope they pass, and try to plot for them passing but I feel like I need a swoop-and-save always in the wings.
Ah, here we clearly have part of the problem. They're in a situation where they would fail most of the time if you weren't engineering things for them to succeed, so they should fail some or most of the time. If you feel bad for railroading them or for removing the challenge from the game by ensuring that they don't fail, stop doing that.
PCs don't need to succeed all the time, especially when the danger isn't lethal. Failure can be instructive and even fun! (Even, dare I say it, . . . "character building"?) Honor is so important in that setting that a moment of lost honor, a recognition that they aren't perfect in all things, can do wonders in terms of future character motivation. Plan for the characters to fail.
That is not to say that they should never succeed or not learn anything, though, but there are ways of doing that without having direct social-roll confrontations or even after failing at all direct confrontations.
First, don't worry about giving them a loyal subordinate with the social skills to take on the courtiers some of the time, and don't worry about fudging the rolls for him up or down if you have to . . . maybe he's talented but new and prone to rookie mistakes or getting rather old and not as fast or perceptive as he used to be. Also, don't worry about having him advise the PCs. However, his advice shouldn't just be "do this"; have him offer multiple options with pros and cons and let things play out from there. Heck, let him be wrong sometimes just so the PCs don't rely on him too heavily. (A sufficiently deep intrigue will have elements he couldn't expect, or that were expecting him. . . .)
Second, give them plots where their bumbling or social weaknesses are strengths. Have enemies overestimate them and plan for the wrong reaction from the PCs, have their bumbling somehow convince everyone that they know more than they do (spooking the enemy into making mistakes), have them accidentally round up all the right people for all the wrong reasons and someone confesses to the plot and then asks how they knew, or just plain have things come to a point where the villains are expecting some nuanced social reaction they can parry and the heroes decide to just charge in and take care of things the old-fashioned way.
There's one more option: The overestimated idiot at the center of a backstabbing circle. In social politics, this is where everyone tries to curry favor with the lord by telling on everyone else. As a result, the lord is spectacularly well-informed about everyone else's secrets and develops a reputation for being an omnicient badass when all they had to do was sit there and look stern and knowing. If your players can handle that kind of information effectively, they'll find ways of taking care of business without ever having to make a social roll they don't like.
Best Answer
I once had a Shadowrun group who hit a truck transporting gold, and they walked away with something like two million nuyen (each) in a campaign where that was more than they had combined through character creation and their careers.
It was somewhat of a mess, but it counteracted itself nicely, because I didn't just let them spend it on anything they could afford-they had to justify finding, and purchasing their new gear, so instead of immediately buying weapon and power foci and cutting-edge augmentations and weapons the massive haul wound up sending them on missions to build relationships and find things that they could then spend their money on; in addition to the copious amount spent on outfitting the team with headquarters and new shiny vehicles so they no longer had to take the bus or drive personal vehicles around on their runs.
Basically, look at the windfall as a stepping stone to future encounters; players probably don't have the relationship with the master artificers or merchants who sell the sort of things they can now afford to buy some of the stuff they want, so they'll have to work to it.
Of course, though this doesn't work in every setting, spending a lot of money at one time tends to be frowned upon in certain places, especially when tax evasion or criminal acquisition is suspected.