The complexity of the labor/savings problem in the US. It is well-known that the optimal investment decision is extremely difficult. In particular, there are many unknowns that are important for deciding retirement decisions--for example, what will be the average performance of the asset classes going forward and how will the covariances between asset classes change. This paper analyzes an apparently simpler problem: how much should people save (in pre-tax and Roth-type accounts) given different incomes and ages in the current system in the US. The authors show that the enormous complexity introduced by the various tax brackets and tax incentives/penalties/transfers in our current system creates a very complex mathematical problem. If you know your age, income, expected life span, expected asset performance, etc., and want to have nice smooth consumption throughout your life, there is an optimal savings strategy, but to get it perfectly right, you would have to do a great deal of computation. People will do the best they can, but the authors suggest that there is a perfect answer if you know these parameters but the math to get there is too hard for a lay person to do.
Tax arbitrage. Arbitrage has several definitions, but generically if you can enter into a transaction that will increase your wealth without taking on additional risk, you can call it an arbitrage. Putting money away pre-tax in a 401(k) style investment when your marginal tax rate is high and then spending it when your marginal tax rate is low is an example of such an arbitrage if you compare it to saving outside of a 401(k). Of course, if you are in a low tax bracket because your income is low, you will get little benefit in the form of tax savings from contributing to your 401(k). This is one reason this type of account benefits some people more than others.
Roth arbitrage Saving in a Roth account increases the wealth of anyone who uses it instead of using a regular taxable brokerage account. In either case, taxes are paid at the time you earn the money, but if the money is placed in a Roth, it is never taxed again. If it is saved in a taxable account, taxes must be paid on the capital gains and interest every year. So if you are long-term saving, it is unambiguously better to do so in a Roth account than in a taxable account. Normally I'd say what's not unambiguous is whether it's better to save in a Roth or Traditional IRA. Most people would say it depends on your income. However, within the constraints of their model, the authors show that the arbitrage for a 401(k)-style savings decision is uniformly larger than that of the Roth. If we believe the assumptions of their model, we should stick with traditional IRA and 401(k) contributions and pass on the Roth.
The nature of the paper. At the end of the day, this is an academic exercise that makes strong (not necessarily true) assumptions about people, about the market, and about the future of the tax system. However, the authors try hard to use all available rules to figure out the optimal strategy given all the complexities of our current system. They use their results to teach us (as individuals an a society) some lessons. To society, they say that the system is too complex for people to use effectively and that the current system pushes people to make some savings/labor decisions they wouldn't otherwise make and that may not be optimal. Moreover, there isn't a coherent logic to who the current system penalizes and rewards if you consider age and wealth. To individuals they have advice like "avoid Roth accounts" as mentioned above.