[AGREE 1. Rent control limits the availability of affordable housing. - I could post "disagree" and quibble that what it does is it limits the availability of housing, period, but sure, this has been pretty well established in the literature with lots and lots of real-world examples.
DISAGREE 2. Tariffs reduce economic welfare. - By and large, sure they do; however, if another country chose to heavily subsidize a product (for example, the way the US subsidizes corn) putting a tariff on that same product could very well counter-act some of the effect of the subsidy and allow local companies to compete with international ones. I probably agree 99% with the original statement if you have to put things into black and white, it gets... black.
DISAGREE 3. Outsourcing to foreign countries should not be restricted. - This is a normative and not a pragmatic statement, as noted earlier. If another country allowed slavery, I'd like to think that we would have restrictions against US companies dealing with said country.
AGREE 4. Floating exchange rates are effective international monetary policy. - I know zip about international monetary policy.
AGREE 5. We should eliminate agricultural subsidies. - See my note on #2! They're more trouble than they're worth IMO, create issues of their own (such as agriculture attempting to sell their surplus into other industries, or by adding extra food to... food like HFCS).
AGREE 6. The gap between Social Security funds and expenditures will become unsustainably large under current policy. - Agree, but many, many years down the line, and it wouldn't take a huge shift in the budget to accommodate this.
DISAGREE 7. Large federal deficits adversely affect the economy. - Define "large". The USA has had a pretty big deficit for years and has been operating just fine. I'd go ahead and opine that much of the time, a large federal deficit is caused by a weak economy, not the other way around.
DISAGREE 8. Welfare should be administered as a negative income tax. - I think the way welfare is administered now is fine, thanks. It's a government program and as such has lots and lots of checks and balances to guard against abuse. The fact that there is still abuse is not a good reason to just throw out all the checks and balances.
DISAGREE 9. The minimum wage increases unemployment among unskilled workers. - Not in the USA, no, and not always. Yes, theoretically minimum wages are price floors on labor and see #1, but in practice if the floor is already below the lowest asking price for labor, the effect is negligible and therefore 9 is sometimes false.
DISAGREE 10. Taxes and permits are a better way to control pollution than pollution ceilings. - I don't get what Mankiw is trying to say here, but cap and trade worked out fantastically well for the acid rain issue and that involves pollution ceilings (and also taxes and permits).