I have done over 5000 puzzles on chesstempo but still can't sense any tactics. So for the past few days I've been making a mental note each time a signal appears (loose pieces, exposed king, potential for double attack, etc.) and try to think of a way to exploit it but to my surprise, I can't find any. What I envisioned when I started doing tactics was that I would reach a point where the tactics would come automatically to me whenever I play a game but that point never came. Although I started doing the mental note thing a few days ago, is there anything I can do to improve it?
Developing tactical ability is a long process. At first you expose yourself to new patterns, try to understand how they work when they are already on the board. You will still not spot it every time it appears in your games. But sometimes you will. And sometimes you will see that you or your opponent cannot play a move because it fails due to a tactical motif you know.
The next step is seeing the potential motif long before it appears and setting it up. It is good that you note weaknesses in your opponent's position. This is the first step towards setting up tactics. You see a loose piece, you position your pieces so that eventually you can exploit that.
It takes a very long time from knowing a pattern to setting it up yourself. Be patient. Sometimes I see a tactic by GMs and I can barely solve it with all the pieces already in position, and then I realise they saw it 10 moves ago and played towards it and all I can do is hold my head.
It may be the case that your training method is not suited for you. Studying random puzzles, not sorted by patterns or some overarching theme, may not be good for you. It is good for pure calculation, but not when you are trying to develop your pattern database.
I think if you a looking for puzzle solutions in-game you are going to have a lot of difficulty off the cuff. I find that because puzzles just drop you in a position, you aren't put in with context, or your own bias (eg; your development ideas).
The above being said, I find that when i look at puzzles they comprise of 4 key materials which are extremely beneficial to game play;
- Mate in N
- Win Material (There are more but these are good beginnings)
I find focusing on Forks, Pins and Winning Material when in game I often fair a lot better.
I have won 4 or 5 games in the last 24 hours (in the first 10 moves) by people just over extending their Queen and me being able to pin their queen between my attacking piece and their King. I find that i can often get a knight to get some solid forks, and i usually just look for overloaded pawns and pieces and try to target them.
Puzzles are great for Mid and End Game tactics however probably aren't a great basis for "training". If you can look at the board objectively without history , bias etc and view the board as a puzzle looking to find the "Best Move" then maybe puzzles might make a good training solution.
The other issue you will find is that the tagging sucks. The amount of Chess.com puzzles that are tagged as "Battery" that has nothing to do with "Battery" is ridiculous, my personal favorite are the Mate in 1 when they are clearly mate in 3 puzzles.
Suggestions; do a few lessons or videos on tactics. I am not suggesting torenting but the Chessmaster XI Grandmaster Edition has a fantastic series of lessons presented by Josh Waitzkin which I find are fantastic at teaching tactics, particularly end game tactics. The amount of games that People stale mate because of poor end game tactics is disturbingly high.
Puzzles are great practice, but one issue with them is that they drop you directly into a position where a tactic is available. That is, you're given a position and asked to find the best move knowing that it will involve some trick to win material or deliver checkmate. In a real game, tactical opportunities show up rarely, and very often the best move (if there even is a singular best move) is just some simple development, making an obvious threat, or defending an obvious threat. There's no indicator that pops up and alerts you that some tactical trick is present.
I think what you said, regarding making note of common scenarios that lead to tactics, is great. The fact that you can't often come up with a tactic is simply due to the fact that tactics aren't usually available. But taking inventory of king safety and potential attacks is a very good thing to do.
Another way to frame it is to always consider all possible checks and captures (both for you and your opponent, of course). Even the ones that look nonsensical, because very often those moves will suddenly become available as the game evolves. This will cover most tactics, and then you can add "moves that threaten a piece" to the list (this is really just "captures" but one move ahead, but you need to think like this to spot/avoid forks). Finally, being aware of when pieces are lined up will help you spot/avoid pins/skewers.
The human brain finds it much easier to recognise patterns that have a name. This is how everyone from Casino card counters to professional Memory competitors develop their skills - they use mnemonics.
It's the same in Chess. Rather than thinking "Hmm, the position this Knight is in seems advantageous in some familiar way", you train yourself to say "Great, I got an Outpost".
As other's have said, you get this from study, not from puzzles or even casual play
Consider the possibility that you might not be seeing tactics because there might not be any tactics available to see. Just because your opponent has an exposed king or a pinned piece doesn't necessarily mean that there's any way to attack the king or to exploit the pin.
You should still definitely check to see whether there are any tactics available in such a position, but you should not be surprised if, nine times out of ten, there aren't any.
Remember that if your opponent is of a similar skill level to you, he or she will also be examining the position for possible tactics. You opponent might have consciously allowed you pin his piece because he couldn't see any bad consequences for doing so. In such a situation, it should not be terribly surprising that you also cannot find any tactics. Possibly the tactics are too deep for either of you to discover at your skill level, and possibly there are simply no tactics to be discovered.
Remember that the opportunity for tactics also depends on your skill level (and, of course, your opponent's). When beginners play, there are blunders galore and many opportunities to execute tactics. When experts play, there are very few piece- or game-winning tactics of the sort found on chesstempo.com. The better you and your opponents get, the fewer tactical opportunities you will discover.