Smith's arguments hold their ground well enough on their own when his premises are accepted. However, there is a lot to be argued about for or against his premises, and unless it is determined that his premises are true then one should not accept the argument he present for economics.
Additionally, Smith's philosophy regarding government and economics seem dissonant in that he prefers government to not be involved in the "free market" of the economy, but does actually believe that government is necessary for making sure that wages are paid appropriately, minting coins, regulating certain institutions, inducing temporary monopolies, restricting loans, restricting banks, etc.
These are the list of actions necessary for governments to be involved in, according to Adam Smith's The Wealth of Nations (compiled by Mark Thoma):
- the Navigation Acts, blessed by Smith under the assertion that ‘defence, however, is of much more importance than opulence’ (WN464);
- Sterling marks on plate and stamps on linen and woollen cloth (WN138–9);
- enforcement of contracts by a system of justice (WN720);
- wages to be paid in money, not goods;
- regulations of paper money in banking (WN437);
- obligations to build party walls to prevent the spread of fire (WN324);
- rights of farmers to send farm produce to the best market (except ‘only in the most urgent necessity’) (WN539);
- ‘Premiums and other encouragements to advance the linen and woollen industries’ (TMS185);
- ‘Police’, or preservation of the ‘cleanliness of roads, streets, and to prevent the bad effects of corruption and putrifying substances’;
- ensuring the ‘cheapness or plenty [of provisions]’ (LJ6; 331);
- patrols by town guards and fire fighters to watch for hazardous accidents (LJ331–2);
- erecting and maintaining certain public works and public institutions intended to facilitate commerce (roads, bridges, canals and harbours) (WN723);
- coinage and the mint (WN478; 1724);
- post office (WN724);
- regulation of institutions, such as company structures (joint- stock companies, co-partneries, regulated companies and so on) (WN731–58);
- temporary monopolies, including copyright and patents, of fixed duration (WN754);
- education of youth (‘village schools’, curriculum design and so on) (WN758–89);
- education of people of all ages (tythes or land tax) (WN788);
- encouragement of ‘the frequency and gaiety of publick diversions’(WN796);
- the prevention of ‘leprosy or any other loathsome and offensive disease’ from spreading among the population (WN787–88);
- encouragement of martial exercises (WN786);
- registration of mortgages for land, houses and boats over two tons (WN861, 863);
- government restrictions on interest for borrowing (usury laws) to overcome investor ‘stupidity’ (WN356–7);
- laws against banks issuing low-denomination promissory notes (WN324);
- natural liberty may be breached if individuals ‘endanger the security of the whole society’ (WN324);
- limiting ‘free exportation of corn’ only ‘in cases of the most urgent necessity’ (‘dearth’ turning into ‘famine’) (WN539); and
- moderate export taxes on wool exports for government revenue (WN879).
What sort of government does these things and is not involved in the economy? In fact it seems clear that most of the functions of the government are having to do with the economy. One might say that the economy is not necessarily the free market, and that Smith only asserts that the government should not be involved in the free market. However Smith himself states that because an unregulated market may result in a monopoly, that it is not really free, and therefore markets must be regulated in order to be "free". Of course, in a free market there are many more (and greater) problems than monopolies emerging (e.g. companies polluting rivers and killing other ones, land-owners being uncooperative and disallowing passage through their territory, etc.). If the solution is to allow the government to intervene in order to make things "free" in the instance of monopolies, why not then here as well?
Essentially, Smith's argument is based on axioms that may be disputed (easily), and his argument is dissonant with itself. While he may be closer to a sound logical reasoning than others, the work he did in the The Wealth of Nations is still a poor starting point for economics.