Pro-forma the land will still be in private hands, thus encouraging people to improve it. (Remember: buildings are not taxed, only the land.)
The government will be very interested in improving the value of land, eg by making saner infrastructure investments, because they automatically get more tax money to play with that way.
With regards to the rental market, people will only rent where they can afford, which is exactly the same as now, what it does change is the amount of profit that landlords can make from each property. If we have a land use tax I'd like to see it increase based on the number of properties you own, which would discourage people buying large numbers of properties just to rent them out.
Again, the purpose of the tax should be to curb the demand for property as an investment. If you do that the increase in house prices should come down, and as a side benefit there's less incentive for companies to expand nationally, which would increase diversity in the marketplace.
Generalising land value tax effectively makes everyone a tenant —land property is abolished. This sounds revolutionary, but since this affects only a minority, I'm not sure how much of a change this would really be. I'm pretty sure for instance that it wouldn't rise the renting prices in big cities.