I service a lot of revolvers, and I'm a big revolver nut, so I've had a lot of opportunities to work on, test fire, tune up, hunt with, carry, you name it with Taurus revolvers.
While I am a happy owner of Taurus all-steel revolvers, there are particular issues you will see. There are inherent design issues for all models, so don't take this list as anything which should really deter you from owning a Taurus revolver, with the exception of the Ultralight models, as I'll explain below.
There are a lot of rumors and hyper-sensationalization floating around the internet about poor machining quality, inconsistent metallurgy, etc. Most often, these are either exaggerated claims of a normal failure issue which can happen with any mass produced brand, or propagation of rumor without any real evidence. Thoroughly use or abuse any revolver and you'll run it loose, and eventually out of time. No brand is immune to that. I also have NEVER experienced poor customer service from Taurus, alternatively, I have always experienced fantastic service, both for personal firearms I have needed repaired, or factory warranty repair/replace issues for customers. They're a little less apt to send out free parts than Ruger might be, but I find them more prone to share freely than S&W. You can look at the revolver itself, or even simply look at its pricetag and tell which models will wear out faster than others - a $280 Taurus or cheaper Rossi or Charter shouldn't be expected to last as long as a $550 Ruger, firearms do have a service life. Of course, much of this is driven by the fact many Taurus models are effectively a Brazilian knock off of S&W models, which many S&W fanboys don't appreciate. Largely, it's just popular to bash on Taurus.
Some of the specific Taurus revolver issues:
1) For their non-steel revolvers, i.e. the Ultralight models, they use a hardened steel bushing around the firing pin and the main pin to protect the softer alloy parts. These particular bushings have been notorious for improper metallurgy vs. their design (too hard/brittle & too thin), with a relatively high rate of brittle fractures, locking up the cylinder, or seizing the firing pin. So the Alloy frame Taurus revolvers, for their intended defensive purposes, are a 100% no-go in my book. I own a couple 85 Ultralights, but after having as many broken bushings come in, I will not carry to protect my life, and recommend against them entirely. Too great of risk. I DO, however, fully trust my non-alloy, all-steel taurus revolvers with my life.
2) The Taurus crane itself isn't necessarily weak, but the main cylinder pin - or rather main tube - is a thin walled tube, very prone to galling, gouging, cracking, etc. The cylinder bushings riding on the main tube are also a weakness in design - not for immediate and catastrophic failure, but for premature wear. There have been specific metallurgical issues in the past which exacerbated this relatively wear prone design. This isn't really a major issue, they simply loosen up faster over use and develop a bit of end shake. But it's a revolver, it's going to have SOME endshake and lateral displacement, AND it does have a forcing cone to ensure alignment of the chamber to the bore upon firing. Nobody likes slop, and everybody likes bashing sloppy revolvers, and a Taurus WILL loosen up faster, but it's very rare they completely go out of spec, AND Taurus will replace/repair them when and if they do. Use it or abuse it, it'll wear out, no matter what is stamped on the side. There are many models out there in which the crane will warp/twist/bend much more easily than the Taurus's.
3) I'm not hugely in love with the locking bolt design, which is the same as the S&W. It's serviceable, but I prefer the solid piece design of a Ruger over the bent leg design of the Taurus & S&W revolvers. I've only ever seen ONE break in a Taurus, and I have seen as many broken/worn/peened bolts in Rugers and S&W's, but it's something which makes me itch a little when shooting high volume, high speed with Taurus & S&W revolvers, which doesn't make me itch when shooting Rugers.
I also have experienced it's very popular for gunshops to lack favor, and even speak poorly, of Taurus firearms. Part of the issue there is Taurus has a VERY inconsistent supply chain. It's common to hear a shop claim "we'd sell more of them, but we just can't get them." Many of the models showing available on the Taurus website as "current production" haven't actually been produced in years. They're still in the catalog, still showing as an option for production, but they just don't make them. That's frustrating for gunsellers because we just can't get a reliable supply, and if there ever IS a warranty repair or replacement issue, you might not be able to get the part or a replacement of the same model since they're not actually in production.
Overall, the products are good for the money. I own several Taurus revolvers, and I do recommend them for budget minded customers and students in my firearms classes. Taurus service is good as well. They do, however, get a terrible reputation online.