They were still using typewriters and tipp ex in season 1, it looked dated before they had got to season 5. I'm not sure it matters much, it's unclear when The Wire was actually set as far as I can tell. There are references to contemporary stuff (9/11 is mentioned in passing when the FBI talk about budget stuff) but I don't think the timeline is a particular focus for the show. It was broadcast in the early to mid 00s but a lot of the source material and research was from the 1980s and 90s (David Simon was a reporter back then) so you just need to tell yourself it's a series of anecdotes cobbled together to give personality to an overall bigger picture. Forget the fact it was filmed in the 2000s, it's the last great piece of 20th century television.
You mean the first great piece of 21st century television