In econometrics, you can certainly find some example of propagated methods by well-known (and highly skilled) econometricians published in decent journals. I am not aware of a theoretical paper but Lalonde (1986) is quite famous for pointing out that currently used methods do not well: He compares for the same dataset experimental methods with observational ones and finds large differences in the field of (causal) treatment evaluation. There is a large literature which did propagate these non-experimental methods which have been used back then and which are often still used today.
Subsequently, there was (and I think still is) a debate about whether propensity score matching is a possible solution (see for example here).
Furthermore, there is a lot of controversy about instrumental variable estimation. The conclusions of highly cited original papers have been disputed. This is probably closest example to your question. Bound and Jaeger (1996, and subsequent papers) have questioned the findings of the well-known paper from Angrist and Krueger (1991; 2700 citations according to Google Scholar) which basically established the instrumental variable method in the applied econometrics literature.
There is also large debate about the appropriatness of so-called reduced form estimates to establish causality, see for example Imbens (2010).
Another big topic is of course about standard error. One can perhaps find a well-known paper propagating p-values. In econometrics, standard error for longer time-series have often been miscalculated (in the difference-in-difference design) due to wrong existing methods, see here. I am however not aware of an original highly-cited paper proposing these methods in that context but I am sure that you will find some examples in this area.
Angrist, Joshua D., and Alan B. Keueger. "Does compulsory school attendance affect schooling and earnings?." The Quarterly Journal of Economics 106, no. 4 (1991): 979-1014.
Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. "How much should we trust differences-in-differences estimates?." The Quarterly journal of economics 119, no. 1 (2004): 249-275.
Bound, John, and David A. Jaeger. On the Validity of Season of Birth as an Instrument in Wage Equations: A Comment on Angrist & Krueger's" Does Compulsory School Attendance Affect Scho. No. w5835. National Bureau of Economic Research, 1996.
Dehejia, Rajeev. "Practical propensity score matching: a reply to Smith and Todd." Journal of econometrics 125, no. 1-2 (2005): 355-364.
Imbens, Guido W. "Better LATE than nothing: Some comments on Deaton (2009) and Heckman and Urzua (2009)." Journal of Economic literature 48, no. 2 (2010): 399-423.
LaLonde, Robert J. "Evaluating the econometric evaluations of training programs with experimental data." The American economic review (1986): 604-620.*