The GURPS 101: Patching Holes series is meant to help players avoid specific weaknesses on their characters. It also is intended to help players identify a series of increasingly broad and effective solutions to a specific vulnerability or issue.
This post is meant to tell you when not to "patch holes" in this fashion. And it's meant to address some of the issues that come from over-doing "patching" by getting too focused on the specific problem.
A "hole" is a specific weakness a character has. Especially if that weakness isn't intentionally built into the character but represents a poor choice by the player. Or it represents a misunderstanding of how to lower your vulnerability to that particular issue.
Don't Patch Everything!
First off, a character with no holes, no vulnerabilities, no disadvantages to lead him astray, and no weaknesses to anything specific is either one of two things: boring, or equally mediocre at everything for a given point level.
Secondly, if you have many holes to patch, you need to start looking at broad solutions to the problem. If you're weak against death, resisted magical spells, disease, poison, and consciousness rolls, plus you're often stunned and knocked down, you need HT. You don't need Hard to Kill, Magic Resistance, Resistant to Poison, Resistant to Disease, Hard to Subdue, plus High Pain Threshold. You need a higher HT. You may also want one or more of those, but you've lost sight of the forest because of your focus on the trees.
Generally, if you have two or more "patches" that have the same root attribute, secondary characteristic, or advantage at their base, consider just improving the base. If you have three or more, you almost certainly are better off improving the base!
I see this pretty often - HT 13  with Hard to Kill 2 , Hard to Subdue 2 , and Fit  - for a net HT 16 for either rolls to avoid death or a base 16 to resist unconsciousness. That's more useful in a narrow sense than, say, one more point of HT for a HT 14  and Fit  and slightly cheaper, too. But it's also less broadly effective - you gain one point on each of the two specific rolls you bought advantages for, but give up a +1 to everything that involves HT and 0.25 added to your Speed, as well.
In a phrase, don't over-patch. Don't be overly focused on improving one area.
Don't Patch Too Deeply
This is a related issue - trying to ensure you cover too many cases, or one case too deeply. Sometimes it's a case of not realizing when you've past "cost effective" into "wasting points" - a real issue in a point-buy game system!
If Fearlessness 1 is useful, then 3 is better and 5 is great. Why stop there - 10, 15, 20!
No, stop there.
You want enough of a trait to either make the weakness go away entirely, or make it less of a weakness. Only patch enough to make the character do the thing you want to do better, better.
If you want a complete solution, go for that. Don't spend more points on the narrow solution or the wide solution than you could get if you just bought the complete solution. This isn't to say Fearlessness 10  is useless, for example. But it's definitely less useful than Unfazeable . It's not as useful as Unfazeable  with Fearlessness 2  just for those Cosmic Terror-having elder things the GM keeps having pop up out of R'lyeh in front of you.
That said, as a GM I deploy plenty of monsters with Magic Resistance 10. That's a very high, very specific countermeasure. I don't use anything higher - it's more point efficient, and therefore a better choice to retain fidelity to the game rules - to buy immunity-type powers instead!
Too many layers. Defense in depth is a great battle strategy - don't pile everything on the front line and hope no one breaks through. Instead layer your defense so what penetrates the first layer must penetrate a second line before it can move on.
Don't try to make sure you have kick after kick at the can for everything. If you really want a do-over if things go poorly, buy Luck  and just get a do-over. That kind of defense in depth is generally superior to layering many different bonuses or many different chances to accomplish the same defensive goal.
This is also the Perfect Defense Fallacy in action. With a limited point budget, anything you spend ensuring that even edge cases don't affect you, or to ensure that you've got a fallback for your fallback, comes out of your broader capabilities. Generally this results in a hole elsewhere. For example, a character with near-perfect combat defenses who is no less vulnerable to magic than a man off the street. Or a character with total resistance to magical domination but a gigantic hole in the form of a (6) self-control roll on an easily exploited disadvantage.
Plus GURPS rarely allows for total and automatic success in an adventuring situation. If it's worth seeing if you can succeed or fail, generally a 17-18 will always fail. Or a 3-4 will always succeed, and might get past your "perfect" defenses. Will 20 is nice, but a 3 on a Will-resisted spell against you automatically overcomes your resistance (p. B241). Don't make the perfect be the enemy of being a capable character elsewhere.
Don't get caught in this trap:
Step 1: Ensure total and perfect immunity to everything.
Step 2: Game ended before I could achieve Step 1.
A word on house rules.
GURPS 101, for me, isn't about house rules or clever solutions. It's the basics you really need to know as a new player, but don't always realize until later.
That said, I expect a lot of comments about a specific house rule on this post, so I want to address them right away.
Some groups house rule that you can "trade in" combinations of secondary characteristics for a higher level of a base stat. The most common example is Striking ST 1 , Lifting ST 1 , and 1 HP  for one point of ST , as they're almost identical in function. But this isn't a rule in Basic Set. Not only that, but some traits don't combine so well. Hard to Kill 1 , Hard to Subdue 1 , and FP 1 , plus an extra 3 points seems like it adds up to one point of HT , but it doesn't - the problem is that Hard to Kill comes with an additional capability - appearing dead while alive and unconscious - that is not rolled into HT at all. A character "trading in" in this manner is actually giving up an ability. So be careful making partial purchases to patch a hole on the expectation you can "trade up" to a better base ability. Only do so if the GM and other players have agreed on this approach before you start buying.