Sometimes intelligent people fail to notice a glaring error. By preventing what I call the "snow blindness" syndrome, you can save time, money, and grief.
When team members overlook details, the resulting errors may be due to one or more of these factors: fatigue, over-familiarity, or poor morale.
Too tired to think straight
Physical or mental fatigue may be due to personal factors, such as a new baby. If this is the case, talk to the team member and try to come up with a solution.
Or is employee drowsiness work-related? Is the team working long hours to meet a tight deadline? Remember that harried, exhausted workers make more mistakes. One solution is to institute a "no overtime" policy for a brief period in order to give your team a chance to recharge.
Seen it all before
Are team members so familiar with the task at hand that they're getting bored and becoming sloppy?
A programmer gave me her unorthodox solution to this problem: Write a small section of pure code first with no comments, and then add comprehensive comments a day or two later (or, better yet, get someone else to add them). Revisiting your or someone else's code, and making sense of it in enough detail to comment on it thoroughly, can identify errors that might otherwise be missed. I wouldn't recommend this as an official standard, but it does emphasize how important it is to encourage coders to revisit their work in a new way to help spot slips.
Regular, officially sanctioned code walkthroughs can be a double salvation on the overfamiliarity front. Pair up programmers working on maximally different aspects of the project, and schedule them to perform code walkthroughs for each other. Not only will a fresh pair of eyes help spot obvious mistakes, but it will also provide more variety in everyone's day.
This forms an important part of so-called extreme programming. If you have the resources available, "third-party walkthroughs"—where programmer B walks through programmer A's code with programmer C—can extend these benefits and provide an extra layer of sanity checking, ensuring that B really does understand what A has done.
Lost their drive
Team members may have poor morale for various reasons, including an abrasive team leader or dissatisfaction with pay or conditions. And when low morale leads to poor motivation, everything starts to slide. That's when the "it's good enough" attitude creeps in, and concentration on details begins to slip.
A small-scale way to lift team members' spirits is by taking them out for a team lunch or a recreational event. Let them know they can trust you and that you'll listen to their frustrations.
On a more tactical level, if large-scale organizational issues are affecting your team's morale, take this up with senior management. Be sure to let your team know that you're acting on their behalf. Even if this doesn't have a practical effect, the knowledge that their concerns are being voiced can help overcome feelings of frustration and disempowerment.
Fight the troublesome trio
Once you and your team recognize these three culprits, you'll be able to spend more time worrying about the details. Ultimately, attending to these details now will save you time later.