Time traveling, simply put, is using the "reset clock" feature in the options menu to change the time and date. This is useful for getting things to happen immediately (e.g. getting fruit to reappear after you've picked it all, getting mail sooner, and so on). In order to do this you will need to pick up the phone in your attic before you wake your character up and click 'Reset Clock'. In order for this to actually work, you also need to set your ds time to the same time you will set it in the game. If the ds time and the game time are different, numerous glitches would happen such as Joan never selling red turnips.
Time travel will not bring characters back to your town, nor will it make a special person reappear in your town on the same day and time. Gracie will come back, but it has to be the exact time you saw her. Like if you get on another character to get more Gracie designs.(and if it is a scheduled person, i.e. Joan or Redd). Also, if you miss a balloon or U.F.O. in the sky, time traveling back to the same point you missed it won't bring the item back, either(unless you turn off your ds and,or dsi)These are just a few problems that can't be solved with time travel.
Weeds do come up when time traveling to the future and some flowers may wither. Cockroaches will infest your house as well, but traveling to the past is easy to get something from Nook's Store that you missed and so on. Be warned: if you time travel too far into the future you will find your town covered in weeds and the residents will be unhappy. Tom Nook's turnip prices will never go above 96 bells, and Joan will only sell them over 96 bells so you never make a profit from white turnips. Your favorite characters may be more likely to move away.
Time travel is almost never a good option. Just be patient.
However, If you need to time travel but only need to go forward or backwards a small distance (e.g. 1 week), do not do it all at once. Traveling forwards or backwards one day at a time enables you to find the 3 weeds that would pop up daily instead of the enduring task of picking out possibly hundreds. You can also look in the shops without missing anything. If you are time traveling to grow a tree, do not time travel four days in advance or the tree will rot. As advised, only travel 1 day at a time. Remember that it takes 6 days for a tree to fully grow. When you want to go back to the original follow the same rule or you will get even more weeds still.
To fix these problems, synchronise your AC:WW clock with your Nintendo DS clock. They should go away.
To synchronise your AC:WW game, you need: A clock, your DS and game. First, change the time on your DS to a random time. Go and play AC:WW and go onto your file for a minute. Save and end your game. Go back onto the DS's main menu and change the time back to the original time (this is where the clock comes in handy). Play your game and check the time. If the time isn't the correct time, Repeat the process. A digital clock is easier to understand becaue: 1. The time is easier to read. 2. As soon as the number changes, you can react quickly. Also, you could use an analogue clock, but the digital clock is easier.