When viewing specifications for a certain camera (link to dpreview's specifications table of some model) how can one estimate what is the lag between pushing the button and taking a shot on that model?
The reason manufacturers don't always publish that info is precisely because those cameras are so slow. If the model is faster than average for that class of camera, you can be assured the manufacturer will tout that ability to no end!
The best way I have found is to do an internet search that includes the camera's model number and the words "shutter lag". You will usually find at least a review or two that mentions the camera's performance in this regard.
A google search for Olympus SZ-31MR shutter lag (that was the camera in the dp review link in your question) led me to the following review which included a comparison between that model and several other cameras in the same market niche. Although each site's methodology may vary and you can't necessarily compare the 'shutter lag' measured for one camera by c-net to the "shutter lag' of another model measured by another review site, you can compare the relative performances of different cameras tested by the same reviewer.
No, there is no way to estimate shutter lag of a camera from viewing its specifications on a review site.
Some review sites have done these tests, but test results are usually under separate header, not in the specifications page. One such review site is www.imaging-resource.com. They have measured the shutter lag in more than one way, allowing for AF confirmation in the lag, and lag when prefocused, and even the lag between a camera power up and first image captured. Especially this last type of lag can be very long on some camera models.
I have done a shutter lag comparison chart between four different cameras in my answer to "What makes a DSLR better than a Point and shoot?" There is not so very big difference in shutter lag between different cameras, not even between P&S and DSLR, if the camera has already focused by half-pressing shutter release. All the numbers were collected from imaging-resource.com camera reviews.
They have not tested Olympus SZ-31MR shutter lag.
If I understand your question, you cannot find such a data in the camera's specifications.
I believe we may be a little off topic here, because only the manufacturer could answer you (or maybe someone with very specific equipement to measure the delay between the button pressed and the shutter opening).
But to be honest, I can't really see the point of measuring this delay.
There are different methods to measuring these types of lag timings. It is also a typical problem with monitors, head mounted cameras and displays, measuring feedback, pendulums, falling objects etc. However, for a camera you can control the trigger electronically and use a real-time millisecond-accurate clock (which is a problem in its own to generate), and display the status for the camera to photograph.
Read more HERE
One thing to note is how much is a long time? if you are busy, you know the time flies and one minute turns out to be one hour. but when you are focussed on something and want action NOW, visually 30-50ms is notable, and if it has auditory feedback 10ms is notable.
Apparently, prefocussed you can achieve twice the visually notable with the fastest cameras, but really need to use mirror lockup for perceivable immediate response, even with the fast DSLRs. Seems the SLT brands might have a potential in this area, even though it seems high end ones atm just are similar to the pro DSLRs (without mirror lockup).
Some DSLR test or comparison websites include shutter lag times in their results. Snapsort.com usually provides this information in their camera versus camera comparisons. Contrary to what some have said in their replies, shutter lag times can be very important for most types of shooting, especially sports, group shots and model photography, where catching the right moment, as seen through the viewfinder, is vital. If the time between shutter button-push and actual frame exposure is too long, that moment is lost.
In many instances, knowing how your subject will react and anticipating when to shoot is helpful, but that only works in specific situations, and is essentially a work-around solution if the shutter lag time is very long. It's always better to have a very short, almost instantaneous lag time, meaning one that is faster than the photographer's reaction time.
Two cameras with extremely short lag times are the Panasonic Lumix FZ150 and the Nikon D3, but I think the "record-holder" is a Sony.