Time is a strange thing. It is derived from the position of Earth relative to the Sun. Among other time definitions we have a minute that is 60 seconds, we have an hour that is 60 minutes and a day that is 24 hours. For the longer measurements we have weeks, months, years, etc.
It sounds all very obvious. There are three problems with our current time system though. The first problem is that it is stitched together with tie wraps and duct tape. The second is that it isn't universal. The last problem (and the most important one) is that your clock is wrong 99.99884% of the time. I'll explain that later.
Our time system is a mess and not accurate at all. Every four years we have to correct for an entire day! You have heard of this. It is done in the leap year, where February has 29 days. It doesn't stop there though. We also have something called the leap second. It basically occurs on demand. The clock will go up to 60 seconds instead of the 59 before it goes to the next hour. For example on June 30, 2012 the clock displayed 23:59:60. Since 1972 it happened 25 times.
UTC is also hilarious. It stands for “Coordinated Universal Time”, but it isn't universal at all. Our time system wouldn't work anywhere else. Take for example on Mars. We have the ambition to start living there in 2023. A day on Mars takes 24 hours, 39 minutes and 35 seconds. Good luck correcting the hell out of that. And if that isn't enough, a Martian year is approximately 687 days long.
I mentioned before that your clock is wrong most of the time. This is true, because your clock doesn't continuously correct for the leap year. That would be weird. However, if you compare that to the position of Earth to the Sun you will notice the planet doesn't just jump a day ahead either (obviously). The actual day you are correcting in the leap year is actually smeared over the four years.
To help with the math of this all I made a simple script that calculates the number of seconds the clock's minutes and the position of the earth are synchronized. In other words, the script shows the length of time where the minutes on the clock are equal to the actual minutes. This is taken over a period of four years and ignores the leap seconds. When you run it, it will say the times are in sync for 1469 seconds (24 minutes).
Some simple additional math shows that 1469 seconds is about 0.00116% of four years (126230400 seconds). So if someone asks you for the time and you leave the seconds out, you'd be 0.00116% of time right (or 100 - 0.00116 = 99,99884% wrong). If you also mention the seconds the odds you are saying it right are even worse.
In my opinion we should abandon all those corrections. They only work for Earth anyway. This means it will be dark during the day sometimes and light during the night. These days we have 24/7 production lines and night shifts, so it wouldn't matter that much. A change like that would render DST useless as well, which I think is another win.
That said, we also should get rid of the time zones. Those are a mess too. There are even time zones with 15 and 30 minute offsets. When we get rid of them, we could easily sync up office hours. Besides that, in this time where everything becomes computerized, it would be a lot easier to create computer programs that use time.
Update: Apparently James May said some stuff on this as well: watch the YouTube video.