When the government uses subsidies, tax credits, and other forms of government favoritism to allocate investment funds, will this action tend to promote productive projects and restrain counterproductive ones?

Ideally, government favoritism has it's advantages if purely implemented.

Practically, however, history has shown that even in the most developed countries, it has been misused to the detriment of genuine economic progress.  

Explanation:

Subsidies

Subsidies is usually injected into the economy to encourage production and consumption in specific industries. On the supply side, government subsidies help an industry by allowing the producers to produce more goods and services. This increases the overall supply of that good or service, increases the quantity demanded for that good or service and lowers the overall price of the good or service. For example, government might decide to subsidize the cost of purchasing personal assistant robots to aide the growth of such industry.

Tax Credits

This is also used to stimulate demand in a young industry (or pioneer industry). This is mainly applied to the consumer side. Consumers are encouraged to buy more when they get a tax return for goods purchased.

This can also be applied to the supply side. When manufacturers are given tax rebates, it helps to lower their cost of production and increase their savings.

All the above point towards the promotion of productive projects.

Counterproductive projects cannot be restrained by government favoritism except government uses same tools adversely by withdrawing them to discourage counterproductive ones.

For instance, most government impose very heavy taxes and stringent business requirements on cigarette producing companies just to restrain their growth. History has shown that where the demand for such product is inelastic, government dis-favoritism will have little effect on the operations of businesses in that sector. Cigarette is an example of products with relatively high price in-elasticity because it's consumption is dependent on habit and addiction.

Other arguments against the use of government favoritism stem from the fact that in real world scenarios, government activities are very political without an exemption to the distribution of resources such as subsidies.

In a market without government favoritism, all are equal in the eyes of the law.  In such a situation, free and voluntary trade results in gains for both sellers and buyers.

One destructive consequence of government favoritism such as Monopoly rights is that it enervates discipline. The firm will possess pricing power that a competitive firm lacks. It need not accept the price that would emerge in a competitive market and is instead said to be a “price maker.” If the firm is interested in maximizing its profit, it will set a higher price than that which would prevail in a competitive industry.

In addition, there is no incentive to become more efficient as there are no competitors.

Value is exchanged but not optimally. Consumers still gain from exchange, but they gain less than they would were the market subject to free entry by competitors.