Elementary S01E15 - S01E21

Elementary S01E15 - A Giant Gun Filled With Drugs

No computers and only a short product placement of the Microsoft Surface tablet.

Elementary S01E16 - Details

No computers

Elementary S01E17 - Possibility Two

Only ordinary computer and phone use.

Elementary S01E18 - Déjà Vu All Over Again

Nothing really computer related. The surveillance footages are correctly used and there is no abnormal "enhance" or similar.

Elementary S01E19 - Snow Angels

No computers.
Because of scratch marks Sherlock deduces that a lock has been picked (see screenshot). It is true, that lock picking leaves marks that are detectable. However scratches on the outside are more likely from keys. Pick marks are only visible inside the lock (and probably require a stronger magnifying glass).

Elementary S01E20 - Dead Man's Switch

This episode only features ordinary computer use, although the interface (at ~ 7:00) feels unnatural. I don't understand why actors can't be told what to type and where to click... It would look more realistic and I doubt it would take much more screentime.

Parts of this episode revolved around a dead man's switch (hence the title). A rapist blackmails the victim's families by threatening to release the rape videos onto the internet. He has an accomplice (the dead man switch) who is supposed to release the videos in case something happens to him. Unfortunately (for the villain) he didn't know enough about programming and gave away his secrets to a real person. A real dead man switch is pretty much impossible to steal or to stop.
The idea is simple: distribute an encrypted file and automate the release of the decryption key. For programmers there are countless ways to do this, but even non-programmers could probably find a way. For example, one could take an online calendar that sends out reminders (often even per SMS) and put the key into the reminder message. If the entry is not moved or deleted in time the reminder message (with the key) would then go to some public place.

Elementary S01E21 - A Landmark Story

Almost no computers. Just the same bad cryptography as in episode S01E12.

A cryptographic message that can be solved by hand (or in the head) is just not secure. Somebody as skilled in computers as Sherlock would never decrypt the message by hand.
If done right, the story wouldn't even suffer. For the sake of some suspense, Sherlock could compute a list of possible messages and then find the right one out of it. Without the correct key that's not even that unrealistic. Take, for example, the encrypted message "kdo". Assume that Sherlock figures out that the message was encrypted with a Caesar cipher. Without the key there are 25 different possible plain text messages (assuming that the encrypted message is not the plain text message). Among the possible candidates are "ibm" (the company), or "hal" (the computer from 2001). The TV show could let Sherlock dramatically rule out some of the messages and finally deduce the correct one.