They're mostly dismissed because they suck. Broadly speaking, I hear about six repeated criticisms (I'm going to lump some together because they ultimately boil down to the same criticism):

(1) The models run hot and/or/because the hiatus is a thing, so the science is flawed. Let's call this the future temps argument.
(2) Temperature adjustments are fraudulent and government scientists are evil. Call this the recent temps argument.
(3) Michael Mann sucks and so do his bullshite proxies, [half-understood spiel from McIntyre]. Historical temps argument.
(4) Even if (1)-(3) are false, AGW will be beneficial and/or not so bad that we should care.
(5) Even if (1)-(4) are false, Al Gore is dumb and AGW is a trojan horse for socialism.
(6) "Consensus," huh? Well what about this aging physicist who never worked in climate and hasn't published in years?

Ultimately, (5) and (6) aren't arguments against the science. They're sort of "talking about talking about" AGW rather than addressing the science itself. I also think that you'd hear more practical solutions (such as nuclear power) if the right-wing would actually bother to think about them instead of going "nah, not gonna happen so lets burn coal forever." Ceding the solvency issue to the left is a self-fulfilling prophecy that leads to an energy debate of "smokestacks vs butterfly farts" and leaves nuclear without a natural constituency even though it still produces over half of our non-emitting electricity (and we don't have much growth capacity left in hydro).

(4) isn't really seriously argued by anyone. Tol had a paper (which was trumpeted by noted Bad Science Writer Ridley) that purported to take an "estimate of estimates" among economists for AGW impacts but he ended up having to walk back almost all of it after he pulled a Mann and got the sign wrong for all of the estimates except his own. And even Lomborg, whose arguments are often misconstrued as supporting (4), doesn't believe in doing nothing about AGW. He has, in fact, called for an international carbon tax funding clean energy research.

(3) is true insofar as it applies to MBH98, which sucked. But MBH98 is old. It's not the only multiproxy paleo reconstruction out there anymore. There are lots of others, and not just by him. Moberg, Oerlemans, Esper, Ljungqvist, Shi, Marcott, etc. You'll find that McIntyre has sort of made a cottage industry of carping on his blog whenever a new paleo paper comes out that it re-uses this or that proxy like Yamal or Sheep or Korttajarvi. But MBH98 wasn't just bad because it used a possibly suspect proxy. The entire point of a multiproxy is to compensate for these things, and if Yamal is one of, say, 1,000 proxies, who gives a rat's arse? MBH98 was bad because it only used a few proxies, and used flawed principal component analysis that over-weighted hockey stick shapes and made its conclusions non-robust to those outliers.

(2) is easily refuted by referencing the raw data for GHCN and ICOADS, the most comprehensive worldwide land and ocean datasets. Raw, they show more warming. Adjusted, they show less. (This sort of bitching is inevitably US-centric because the US record has specific historical reasons for being adjusted, as painstakingly explained by the papers that don't get linked in breathless Heartland blogs and Steve Goddard madposts.)

(1) is a somewhat fair criticism to make. (I say "somewhat" because the "models" we talk about are usually averages of multiple model runs, and individual model runs often contain hiatuses of 15-20 years. Obviously we here in reality are only getting one run.)

But it's a criticism that the scientists themselves are making, and have been making for years now, in the literature. They're already hashing it out, and the models are already being adjusted. The issue here is mostly that capital-S Skeptics (as opposed to mainstream scientists publishing things that are walking the projections back a bit, who are really the equivalent of "skeptics" these days) aren't really contributing anything except gleefully tallying up every paper as an "excuse," apparently expecting that the hiatus should disprove AGW and anything else is an "excuse," which misunderstands both the weight of the evidence behind AGW and the burden for overturning rather than modifying an established theory. I chalk it up to the predilection of skeptics for treating "natural variation" as if it's both a satisfying and limitless explanation. Any alternative not only has to explain the hiatus, it has to explain what caused the spike from 1970-2000. Contrary to the "there are a million things that affect climate" folk wisdom, there actually aren't a whole lot of things that affect it on that scale in that time frame.