Can I quickly view other computer’s Event Logs?

…Yes. There are at least 3 ways I can think of right now.

Method #1

The easiest way is to run the command

​eventvwr.exe ''computername

where computername is the name of the computer you want to view.

Method #2

Another way is to run eventvwr.exe and then right click Event Viewer (local) and choose Connect to another computer.

For some unknown reason, if you run eventvwr.msc (.MSC is the file type of most Administrative Tools, as they are mere Snap-Ins within an MMC console) you cannot perform the previous tip. You’ll need to enter it in a different way:

​eventvwr.msc /computer=computername

where computername is the name of the computer you want to view.
(Thank you Steven G. Yarnot for the add-on)

Method #3

A third way is to open a new MMC console, choose Add/Remove Snap-Ins, and add the Event Viewer Snap-In of all the required computers you want to look at.