In the beginning, when Supernatural first premiered on September 13th, 2005, it was about two brothers hunting monsters and trying to find their father, John Winchester. Sam was out of the family business but Dean pulled him back in and Sam lost everything shortly after. They followed clues from their father and they went after monsters. But later in the series, bigger things happened.
Fans are introduced to new hunters and there's no organization between them. There's no coordination for the big events, including the apocalypse, every time it almost happened. Instead, they continue hunting monsters and the big things catch them by surprise every time. The lack of organization, protection, and collaboration in their hunting strategy makes no sense.
There's No Hunter Handbook
The Winchesters rely on accounts from other hunters, John's journal and other hunter journals, lore they find online and in books, and later on, they have the Men of Letters bunker and archives. There's no centralized rulebook, though. Nothing that every hunter can follow if they take up the charge.
The Men of Letters aren't even introduced until Season 8. The bunker offers a more centralized location for information but it's still no handbook. The girls who end up with Jody (Alex, Claire, and Patience) are the only hunters the fans see get formal training from someone who knows what's up. Anyone else in the series learns from their parents.
No Central Headquarters
For most of the series, the Winchester brothers only have the Impala as a reliable place to store their things or sleep at night. There's Bobby's house, the Roadhouse bar, and various hotel rooms but no real place to call their own until the Bunker in season 8. The Bunker is a secret, though and that doesn't help their hunting strategy much.
Sam and Dean often meet other hunters or find people who have been alone due to monsters killing their families. There are children who lose their parents and become hunters, and they have no place to go to learn. There's no rendezvous location. It doesn't make sense.
They Rely On Nefarious Means To Make Money
Sam and Dean are shown hustling pool or running credit card scams to make their cash. They always stay in motels and pay with cash so as not to be tracked. The fake names on the credit card scams also help with that. But there are ways they could run a legitimate business online, through Bobby, or later by using the Bunker.
Bella Talbot sold her services as a medium and Sam knows a lot about magic and witchcraft. Dean could make money running security. They could find and sell non-dangerous mystical items. They could even learn to invest in stocks online. There are a lot of better and more reliable ways to get by aside from the ways that they do.
They Lack Protection From Their Enemies
The Impala is protected, they have tattoos, and Castiel brands their ribs so that angels cant find them in Season 5. The Bunker provides some protection after season 8, but since Sam and Dean don't know all of its features from the start, it's used against them by the British Men of Letters, and those features they don't know about almost result in their deaths.
Sam and Dean grew up in the hunting life. It doesn't seem prudent that their only means of protection are physical weapons and a couple of tattoos and amulets. They live in a world of magic and technology that they utilized far too late. They later learn about hex bags and have some help from Rowena. All in all, though, their enemies seem to find them all the time.
Scarce Amount Of Formal Training
Sam and Dean fight to save the world on a regular basis. Many people have depended on them to survive and yet they've never undergone formal fight training. There are times when they are beaten nearly to death where they could have used formal training. There are more people they could have saved as well.
Many fights could have turned out completely different. They learn lore as they go instead of studying up regularly and they eventually learn to use magic in their endeavors as well. However, it takes until very late in the series for Sam to learn to use magic regularly.
No Relationship With Law Enforcement
Sam and Dean have found themselves in the clutches of the FBI, Homeland Security, and local police several times. They're constantly at risk of arrest and this works against them because it means they can't go back to the same place twice. They've had to disappear, fake their deaths, and make up constant stories.
A relationship of some kind with law enforcement could have had them working with the police instead of constantly against them. They develop a relationship with Jody Mills and some other local sheriffs as well as a few friends along the way that show this to be true. If they'd expanded those relationships or had them from the beginning, their lives, and their hunting strategy, would have been a lot easier.
Drinking Problem
Sam and Dean (especially Dean) constantly drink as a coping mechanism for all the terrible things they've had to deal with in their lives. They often need to make life or death decisions quickly, including whether or not to kill their friends. Drinking as much as they do is bound to cause problems with this lifestyle but somehow it never does.
It makes no sense that people at their age that have been drinking as often as they do wouldn't have some serious side effects. And it makes no sense for the saviors of the world to be constantly drunk.
They Use Subpar Fake IDs
Sam and Dean have a wealth of IDs for different personas, as do most hunters they come across, but they use rockstar names or other famous people. Their IDs have been rejected at times, leaving them to resort to breaking and entering.
The Leviathan used their strategy against them when they copied Sam and Dean and went on a killing spree. Then, when Frank Devereaux told them to go simple, they left that strategy behind as soon as their names were cleared.
The Recognizable Impala
With no real jobs or steady income, it stands to reason that John Winchester's old Impala is probably not the greatest vehicle for cross country travel. It guzzles gas and needs constant maintenance and everyone knows that they're in town when they see that car.
There's no technology, and this has made the car easy to steal, which has happened many times. By relying on this old car, they also have to deal with the added time it takes to get around to the various places in the country where they hunt monsters.
No International Collaboration
When the British Men of Letters came to town, they had Sam and Dean at a huge disadvantage. Had there been more organization and international relations among the hunters in the USA, this could have been avoided. Their appearance and Eileen's story about the Banshee in Ireland when she was a baby are proof that there are monsters in other countries, but the British Men of Letters are the only ones who have ever shown that there were hunters elsewhere.
Sam and Dean save the world from an apocalypse several times but never learn about hunters in the rest of the world. They never visit other countries and Eileen appears to be the only foreign hunter who stuck around in the USA. If the Winchester family business is all about "saving people, hunting things," then why are they only doing so in one country?