It's a broad question, I'll take a stab at it.
The Talmud represents Jewish "law and lore", as one writer put it. Those interpretations of the Bible that have legal force still do; the other material, less so. So I'd distinguish between "Oral Torah" and the narrower "Oral Law."
Do we now dismiss parts of the Oral Torah as incorrect?
Some pages of the Talmud are full of folk medicine, which today we don't use. Already in the 900s, Rabbi Sharira Gaon wrote that the sages of the Talmud were incorporating into their text all the wisdom at their disposal, which included medical thinking from that time that has since become outdated. Today (whether the year is 900 or 2015) we are obligated to use whatever medical treatments are deemed appropriate by today's medical mainstream.
Most rabbis will still study the medical pages of the Talmud, perhaps with a few shrugs -- it's interesting to see how they approached the problems, and it's amazing what a sophisticated legal system they could develop despite the scientific challenges of the era. (A more cautious, traditionalist interpretation would say "maybe this worked in their time and place, but we must use the medicine that works for us.")
The trickier question becomes laws in the Talmud that appear to be based on scientific understanding. The one everyone loves to quote is about killing gnats on Shabbat because they don't reproduce the way normal animals do. There are broadly three approaches:
A. The rabbis could never have been wrong about science. In the case of gnats, maybe they were using terminology popular to the common folk of their day (which today we'd call scientifically obsolete), but the underlying law intended was "animals, as defined by sexual reproduction visible to the naked eye", which hasn't changed. Alternatively: The same way why-bad-things-happen-to-good-people is beyond our comprehension, we're stuck just not understanding that passage in the Talmud.
B. The law is "on Shabbat, you may not kill animals that reproduce sexually." That law has not changed, the application has. 1500 years ago they thought that gnats weren't included, and today we know they are, so our practical advice regarding gnats has since changed.
C. When the Talmud was completed -- let's say around the year 500 -- certain laws as stated were locked into place, which we still respect. (A twist on this would be: the Torah's prohibition on killing "animals" applied to "animals" as the term was understood in ancient culture.)
On a given issue, you'll see any combination of A, B, and C applied today, depending on who you ask.
One high school student who was disturbed by the gnats-on-Shabbat statement consulted with the late Rabbi Emmanuel Gettinger, a Talmudist of the highest caliber and an astronomy enthusiast. Rabbi Gettinger replied:
Is your question one on Jewish law, namely, what do we follow if the legal statement appears to have been predicated on obsolete scientific understanding? [I.e. do we apply B or C above.] Or is it a philosophical one, if the rabbis of the Talmud had so much Godly wisdom, how could they have been wrong about science?
Rabbi Gettinger was prepared to deal with both of those conflicts.
Does this take away from the holiness of the Oral Torah?
Some rabbis will say you can skip certain passages and still say you completed "the Talmud"; but generally, no not really. It gives you an appreciation for how much effort went into study and complex legal codes, despite the scientific limitations of the day. It's also plausible that certain discussions (e.g. the laws of mythological creatures) were intended simply as theoretical constructs (thought experiments) to best understand the details of the underlying laws, which can then be used to apply those laws to today's technology. (E.g. if you have a precise legal definition of "cooking" on Shabbat, you'll know whether it applies to microwaves.)
Is it heretical to say that the Oral Law was influenced by the cultures of the time, for example with regards to women etc?
Again I'd distinguish between lore and law. A story of an interaction between a rabbi and his wife ... certainly culture comes into play, and it's not always clear-cut what lesson to take from that story. My personal preference is to read the story in whatever way gives it the most significance.
Some of the law is of biblical force. The same way that "an eye for an eye" means restitution, according to the Talmud, "you absolutely must dwell in a sukkah" was only addressed to men, not women. We accept that binding interpretation of the biblical law.
Some of the law is of rabbinic force, which we again don't have the power to change today. The rabbis of the pre-Talmudic period obligated men, not women, to pray three times a day. We don't have the authority today to suddenly give women that same level of absolute obligation. (Would we want to is a different question.) If you feel better crying bitter tears that the rabbis back then were outdated and boo-hoo they made the wrong law, but we're stuck with it, well that's your prerogative; personally I prefer to figure there was some universal wisdom that went into it. (Keep in mind that women in many pre-industrial cultures spend a significant part of the day gathering water. Between that and childrearing, it may not have been feasible to obligate all women to pray thrice daily. If a woman today is up to praying thrice daily, by all means that's a wonderful thing and we support it.)
The famous example that everyone loves to volley around is women reading the Torah. "Theoretically it's okay, but don't do it because it's dishonorable", says the Talmud. Those on the left of Orthodoxy will say that statement was predicated on cultural norms, "but today when women are Fortune 500 CEOs there's no such dishonor." Those on the center and right refer to this as a straw-man interpretation of the Talmud, and would say that the "dishonor" described is not predicated on culture. (In this instance, the Talmud also says that some women had signet rings as they owned their own businesses, and a woman who out-earned her husband could demand financial independence. The "dishonor" here would be that the men in the room, who were supposed to be more-obligated to study and spending more hours doing so, are doing a lousy job at Torah reading.)