Where can NH do better? Some of these are not surprising, but some you may not have been aware of:
1) NH has the 2nd highest property taxes in the country once you use the right measure. NH also has the 2nd highest corporate income taxes in the country. I think the Tax Foundation's measures actually overstate how good NH and AK are. Once you exclude gas taxes and use the right measure of the size of the state economy, Tennessee, Texas, South Dakota, Colorado, and Alabama all have lower total taxes than NH, and Alaska ranks 19th.
2) Fiscal decentralization. NH is a little below average in terms of how much revenue is raised at the local rather than state level. Only 34% of taxes are raised locally in NH now. This was probably higher before the statewide property tax came in. VT is the most centralized state in the country, BTW; CO is the most decentralized.
3) NH is good on gun laws, though not quite the very best (AK is overall). NH has child access prevention laws and gun dealer licensing and could be better on transporting handguns in your car (you need a CC permit, which almost makes permit-less open carry pointless).
4) NH has mandatory alcohol server training and keg registration; many other states do not.
5) NH could decriminalize the first marijuana possession offense. If Mississippi can do it, surely we can. A narrowly crafted bill that doesn't try to do too much should be able to pass. Some states also make small-scale marijuana cultivation a misdemeanor; it is currently a felony in NH.
6) NH doesn't require teenagers to wear a helmet on a motorcycle, but it does require them to wear a helmet on a bicycle!
7) NH authorizes authoritarian sobriety checkpoints! Gah!
8) Social gaming, such as playing poker with friends, is illegal in NH! Whaaa...? "Aggravated gambling" is also a felony in NH, and slots, casinos, and racetracks have not been legalized.
9) NH does not have tax credits or deductions for private school scholarships, which a few states do have.
10) NH requires private schools to receive explicit approval from the state before they can operate! Most states don't have this stupid law.
11) NH's standardized testing, notification, and recordkeeping requirements for homeschoolers are still more onerous than most states'.
12) NH has a state wetlands program and associated regulatory statutes.
13) Unfortunately, NH is now one of the few states with a higher-than-federal minimum wage. Let's hope Republicans man up and repeal this if they get elected again.
14) NH does not allow health insurers to turn down individual applicants ("guaranteed issue"). NH also requires small businesses to provide COBRA and mandatory group conversion coverage. Most egregiously, NH is one of the 25 states that mandates direct access to specialists, a regulation that increases health insurance costs. NH also licenses medical plan directors and mandates that health insurance cover numerous benefits, amounting to roughly a 45% increase in premiums, which is one of the highest in the nation (compare Idaho at 21%, Delaware at 25%). This is a major area: in terms of helping the less fortunate, repealing these regulations is probably the most important thing we could accomplish.
15) NH now of course has a comprehensive smoking ban even more restrictive than California's. At least it's not as bad as RI, NY, OH, or NJ. NH also prohibits employers from discriminating against smokers, even prohibiting them from charging them higher health insurance premiums!
16) NH has deregulated electricity, but not natural gas, telecommunications, or cable.
17) NH currently licenses 25 different occupations, which is about average. Colorado licenses only 11, Pennsylvania 13, Michigan 14.
18) NH of course has a state monopoly on distilled spirits; however, NH's effective tax rates on spirits and wine are the lowest in the country, so this might not be the thing to attack.
19) NH has a 3-day waiting period to get married, which seems a bit silly.
20) NH has overly strict regulations on grassroots PAC contributions to candidates and political parties. Grassroots PACs are funded by individuals, not corporations, and should be viewed as a positive part of a competitive political system, IMO. NH's regulations on corporations & unions are just as strict or stricter, though.
These suggestions are things that I think could be done relatively soon in NH, because they are all areas where NH is no better, or even worse, than the average state. There are plenty of areas where NH is better than the average state - mostly in government spending, taxes, and employment. But although NH doesn't spend a lot, it regulates the economy in many ways that I never realized.