The very first version of Microsoft Word for Windows was considered a "death march" project. It took forever. It kept slipping. The whole team was working ridiculous hours, the project was delayed again, and again, and again, and the stress was incredible. When the dang thing finally shipped, years late, Microsoft sent the whole team off to Cancun for a vacation, then sat down for some serious soul-searching.
What they realized was that the project managers had been so insistent on keeping to the "schedule" that programmers simply rushed through the coding process, writing extremely bad code, because the bug fixing phase was not a part of the formal schedule. There was no attempt to keep the bug-count down. Quite the opposite. The story goes that one programmer, who had to write the code to calculate the height of a line of text, simply wrote "return 12;" and waited for the bug report to come in about how his function is not always correct. The schedule was merely a checklist of features waiting to be turned into bugs. In the post-mortem, this was referred to as "infinite defects methodology".
To correct the problem, Microsoft universally adopted something called a "zero defects methodology". Many of the programmers in the company giggled, since it sounded like management thought they could reduce the bug count by executive fiat. Actually, "zero defects" meant that at any given time, the highest priority is to eliminate bugs before writing any new code. Here's why.
In general, the longer you wait before fixing a bug, the costlier (in time and money) it is to fix.
For example, when you make a typo or syntax error that the compiler catches, fixing it is basically trivial.
When you have a bug in your code that you see the first time you try to run it, you will be able to fix it in no time at all, because all the code is still fresh in your mind.
If you find a bug in some code that you wrote a few days ago, it will take you a while to hunt it down, but when you reread the code you wrote, you'll remember everything and you'll be able to fix the bug in a reasonable amount of time.
But if you find a bug in code that you wrote a few months ago, you'll probably have forgotten a lot of things about that code, and it's much harder to fix. By that time you may be fixing somebody else's code, and they may be in Aruba on vacation, in which case, fixing the bug is like science: you have to be slow, methodical, and meticulous, and you can't be sure how long it will take to discover the cure.
And if you find a bug in code that has already shipped, you're going to incur incredible expense getting it fixed.
That's one reason to fix bugs right away: because it takes less time. There's another reason, which relates to the fact that it's easier to predict how long it will take to write new code than to fix an existing bug. For example, if I asked you to predict how long it would take to write the code to sort a list, you could give me a pretty good estimate. But if I asked you how to predict how long it would take to fix that bug where your code doesn't work if Internet Explorer 5.5 is installed, you can't even guess, because you don't know (by definition) what's causing the bug. It could take 3 days to track it down, or it could take 2 minutes.
What this means is that if you have a schedule with a lot of bugs remaining to be fixed, the schedule is unreliable. But if you've fixed all the known bugs, and all that's left is new code, then your schedule will be stunningly more accurate.
Another great thing about keeping the bug count at zero is that you can respond much faster to competition. Some programmers think of this as keeping the product ready to ship at all times. Then if your competitor introduces a killer new feature that is stealing your customers, you can implement just that feature and ship on the spot, without having to fix a large number of accumulated bugs.