Let's start small:
Use ziploc bags to protect individual items or groups of items. This has the benefit of keeping your gear organized, in addition to keeping it dry and protected from animals, and keeping perishable supplies a bit fresher. Items that you don't get into frequently can be even further protected by using vacuum-pack heat seal bags.
Label anything perishable with its expiration date and the date you packaged it. Label your other bags with any pertinent information. If you're truly OCD like mine, you can mark a min/max on the bag. Be sure to go through them regularly and rotate or replace anything getting close to its date. Inventory your supplies and bring anything at or near its "min" level back up to "max." This works particularly well with things like medical supplies and first aid gear, food items, firemaking supplies, and other things that are especially moisture sensitive.
If you're in a position where you're looking for a new bag, consider looking for one that is waterproof/water resistant, or waterproofing your current bag. There is a mind-blowing variety of waterproofing treatments available. Your local camping or sporting goods store would be one of the best places to seek a recommendation. The specific waterproofing you use will depend on the material you're treating, the method you want to use for application, and what may or may not be legal in your state. Learning to waterproof items is also useful for treating gear itself, like ditty bags and tents.
For dedicated gear that you're not planning to pack, look at alternative storage containers. Ammo cans with gaskets are wonderfully weathertight. Make sure that the gasket is in good shape, pliable and with no cracks or breaks. If you drive a truck, in-bed toolboxes with seals and tight fitting lids hold a plethora of gear, and keep it secure and dry. Sporting goods stores that cater to campers and river runners sell "dry bags" and "dry boxes" which are truly watertight storage containers, the ultimate in gear protection, but nigh-useless if you have to actually carry them anywhere.
Consider storing items like your BoB inside another container. This is a spin-off of a trick Grandma used for as far back as I can remember. She had a large plastic tote in her trunk that held most any emergency supply an old farm girl could need. In my wife's truck (actually a small SUV), all of her emergency gear lives inside a locking Rubbermaid tote behind the back seat. It is weathertight, and can be secured with a simple padlock. It is large enough to hold her Car Survival Kit, a 72 hour food kit, fire extinguisher, and basic tools. Grandma's wisdom lives on.
As to my friend's original problem, periodically check the weatherstripping and seals on your doors, windows, trunk, and hood. Doing this at the same interval as your oil changes is an easy schedule to remember. The seals should be elastic and pliable, with the exception of the plastic "scrapers" at the base of windows that roll down. There should be no gaps or cracking. The seals should hold firmly to the metal of the car body. Windows that don't roll down should have all of their trim pieces, and a solid bead of adhesive between the glass and the car body. Sealant to go around glass is available at automotive supply houses, as is replacement weatherstripping and any needed adhesives, for a quite reasonable price.
Take care of your gear, so it can take care of you.