I think the fundamental question that isn't being asked is, "What is the purpose of time tracking?" Depending on your answer for your group should influence the answer.
For my group, we work on very large features: an individual feature takes on average 9 months to 1 year to develop and around 2000 hours of estimated work.
I view time-tracking to have 3 general purposes (one or more of which may apply to a particular project):
1) Time-tracking to improve future estimations. This is the one I currently use most often. We spend a fair amount of time up-front developing a detailed effort estimate in both hours and elapsed time. Generally engineers are assigned to project on a full-time basis (we find that increases efficiency rather than mind-share on multiple projects, but that would be a different thread). Instead of having engineers do time-sheets we have project managers mark at the end of each week how many FT and PT engineers worked on the project. We find that using that to measure actuals against planned provides a high relative accuracy for looking at where we need to improve our estimations in the future.
2) Time-tracking for billable work. This is best used when a contract requires that we demonstrate actual hours performed to complete a project. For the purpose of billable work, .5 hours has always proved sufficient for customers.
3) Time-tracking for auditable work. Basically, the same as #2, but applies especially for government or other contracts where the time spent on a project can be audited by the customer even in the case of fixed-priced contracts. The same granularity of .5 hours has always sufficed to demonstrate area of focus.
Generally speaking, I have found that the smaller the time granularity you require of team members the lower your overall accuracy. Additionally, a smaller granularity may lead the audience to perceive a higher level of accuracy then there really is. When required, stick to .5 - 1.0 hour granularity. The audience understands that there is some play in that number but that it provides a general output of how time is spent.
But, only engage in time-tracking once you understand what the purpose is for tracking time - don't do it just to "monitor" or tick-a-box that you are doing it. You will not know what to measure and will likely fall into a trap over-enforcing an onerous policy that isn't delivering value.