I agree. I'd go further and say that the NY Times is the world's best English-language newspaper, with the possible exception of the Financial Times. I think much of the criticism comes from two issues:
1) Newspaper journalism is very hard; look at how much new research (i.e., almost everything they publish outside the editorial page) they publish every day; they're going to get a few things wrong and make a few errors in judgment. However, name a paper that does this job better.
2) The ideological right-wing, trendy in some places (e.g., News Corp publications such as Fox News and the Wall St Journal), in their effort to discredit any source of information for their followers but themselves, have tried to politicize the NY Times. After all, the NY Times prints facts, and those are always a threat to any ideology.
That said, some errors, such as during the leaup to the Iraq War, are inexcusable (but what papers did better?[1]). They're the best, but they could improve a lot.
[1] I think the one answer might be McClatchy's (a leading owner of local papers) DC bureau. Highly recommended for their courage on unpopular questions and for their integrity. A very underappreciated resource: http://www.mcclatchydc.com/
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The Economist and NY Times do two different jobs. The Economist provides analysis; the NY Times generates and presents new knowledge (i.e., journalism), essentially for you to do your own analysis.
For example, the NY Times researches and breaks the story on NSA wiretapping; the Economist provides context and analysis of it (think about it: Have you ever seen the Economist break a story?). The NY Times interviews the head of the NSA, telecommunications companies, privacy adocates, etc. and provides their responses to you. The Economist summarizes and analyszes the responses (think about it: how often do you see quotes in the Economist?).
I'm not criticizing one or the other; both have their place. My perspective: The Economist approach is more efficient (someone does the analysis for you) but is more prone to bias (e.g., they apply their free market ideology everywhere). The Times approach is essential (someone has to create the new knowledge) and less prone to bias, but you need to read a lot more to understand the same story.