Ideally, in the opening you'd like to play rather quickly to conserve time and energy for more important moments later in the game. However, it is precisely this that can lead to critical moments being passed over without either player's even vague recognition.
Normally this happens because play derails ever so slightly from a standard theoretical line that both players simply don't notice that anything is different. However, looking out for such differences is exactly a way to pick up an easy win every now and again, as well as saving yourself some potential embarassment.
About a year ago, I played a game (with the White pieces) that began as follows:
1 e4 e5 2 Bc4 Nf6 3 d3 Bc5 4 Nf3 Nc6 5 c3 d5? 6 exd5 Nxd5
Now, this is similar (but not identical) to a popular line 5...0-0 6 0-0 d5 7 exd5 Nxd5, which is thought to be roughly equal. Not suspecting anything, I very quickly played 7 0-0 0-0, when play transposed back into the aforementioned theoretical variation, It wasn't until I got home that I notice the following possibility:
I went on to win this game regardless, but I could've saved myself a lot of trouble.
Looking at my recent Over The Board games, I couldn't find too many examples of these things happening to me recently. However, when I was younger (and weaker), it occurred far more frequently. The following games were played in 2014, about a month apart.
1 e4 e5 2 Nf3 Nc6 3 Bb5 a6 4 Ba4 Nf6 5 d3 g6 6 0-0 etc.
(The normal line is 5...d6 first, and after 6 0-0, only then 6...g6.)
1 e4 c6 2 d4 d5 3 Nd2 dxe4 4 Nxe4 Nd7 5 Ng5 Ngf6 6 Bd3 e6 7 N1f3 Be7 8 Ne5 0-0 etc.
(In this case, I recognized that Black has played 7...Be7 instead of the usual 7...Bd6. Knowing that this wasn't the main line, I searched for a way to punish it, and landed on 8 Ne5?. Instead, White should just continue normally, when he can claim an advantage due to Black's slightly passive development scheme.)
In my first example, no points (results-wise) were lost by either side, as White ended up winning regardless of the missed opportunity. However, in both of these past two cases, I ended up winning the game after my opponents each missed a chance to win a clear pawn. They each potentially missed the chance to gain a clear point, while my score over those two games could easily have been 0/2 instead of 2/2.
I think it's worth it (in classical time control games) to spend at least a minute on moves in the opening to avoid such things happening. It can often be beneficial to try and step back and examine the position as though you'd never seen it before; removed from all biases and notions. This way, it's far easier to realize "Hey, wait, there's a pawn hanging", than if you'd never eve paused for thought in the first place.
All of the above tactics seem totally obvious in hindsight. However, at the time, clearly neither me nor my opponent were thinking in terms of tactics, but merely rotely following "standard procedure", despite the subtle, yet drastic changes to the position.
Appendix A: The above phenomenon can also occur on a smaller scale. The following game was played in 2015, where both players where playing "automatic system moves", and failed to notice a positional threat as it passed by. I had the Black pieces:
1 d4 Nf6 2 Nf3 e6 3 Bf4 c5 4 c3 b6 5 e3 Bb7 6 Be2 Be7 7 0-0 0-0 8 h3 etc.
The game was eventually drawn. Nothing too major this time, but 7...Nh5!, winning the Bishop pair, would have equalized comfortably (at least).
Now, some exercises:
J. Polgar-Spassky, Budapest 1993
1 e4 e5 2 Nf3 Nc6 3 Bb5 a6 4 Ba4 Nf6 5 0-0 Be7 6 Re1 b5 7 Bb3 d6 8 c3 0-0 9 h3 Nb8 10 d4 Nbd7 11 Nbd2 Re8 12 Bc2 Bb7 etc.
The theoretical line instead goes 11...Bb7 12 Bc2 Re8, transposing into the game. Why is that move order more accurate?
Madan-Jones, Coulsdon 2008
1 e4 c5 2 Nf3 g6 3 c3 d5 4 exd5 Qxd5 5 d4 Bg7 6 Be3 cxd4 7 cxd4 Nh6 8 Nc3 etc.
...Nh6 is a common move in this variation, but not precisely here. Why?