When people talk about democracies, it's common to think of the US Constitution as the "defining point of democracy". While the US is the first modern democracy, its laws is far from perfect. In fact, it may be one of the worst of modern time! I will briefly go through the following.
Corruption
A near-ideal democracy would have a roughly linear positive correlation between the fraction of voters who support a policy and the possibility of the policy being passed in the legislature. But in the US, the line is flat at about 30%. A representative democracy wouldn't have a perfect correlation, because the general public is unable to be informed on all topics; fluctuations are normal. But a flat line means that the opinions of the people don't matter at all. This does not make sense in any type of democracy.
According to the study, the influence of economic elites and business interest groups on politics is rather high with a rough positive correlation as opposed to the flatline for the general public, making the US an oligarchy rather than a democracy. Mass-based interest groups have discernible impact on policies, but are still trivial compared with economic elites and businesses. About three billion dollars are spent yearly by large "politically active" businesses to bribe politicians to pass policies for their interest. While businesses should have a say in legislation, it is unacceptable that they have superior dominance over public opinion.
The Senate
The Senate of the USA consists of 100 members, with 2 from each state. Two senators from California represent 39 million people while the two from Wyoming represent 500 thousand people. The founding fathers never could have imagined such a huge a difference between the population of states.
Some people believe that the Senate helps against populism as opposed to the House. Although the number of Senators for each state do indeed not correspond to the population, this has no correlation whatsoever with preventing populism and doesn't serve an obvious purpose. It only "helps" by giving completely unproportional voting powers to people based on their location, period.
The Senate also suffers from the fillibuster. Passing a bill in the Senate has a few steps: Firstly the Senators must agree to vote, passed at a supermajority. Then the Senators actually vote on the bill. Those who are against the bill will just disagree to vote altogether, effectively requiring all bills to have a supermajority support to pass which is nearly impossible as the two dominant political parties almost always oppose each others' bills and neither have a supermajority in the Senate.
The Electoral College
The electoral college makes it possible to win an federal election without winning the national popular vote. It also, similarly but not as badly as the Senate, represent the people of each state disproportionally as each state has two extra electoral votes regardless of their population.
A subtle but serious problem with the electoral college is that electors' listening to the votes of the people is only a tradition. Legally, electors can vote however they want, meaning that the US is not theoretically a democracy. This hasn't happened before, but this is one more to the list of problems in the constitution, and is a potential for disaster.
Plurality Voting
Single-winner elections in the US uses what's called "plurality voting", where each voter casts one vote to their favorite candidate and the candidate with the most votes win. This contributes to the partisan dualopoly (not an actual word, but it basically means "monopoly" but with two rather than one) as voters who support smaller parties will undergo the decision of choosing their honest favorite or one of the two big parties that most closely ressembles their favorite. As it's hard to gather votes for smaller parties, and thus there's a small chance of them actually winning the electron, many voters strategically vote for the big party in order to not be "taken over" by the big party that they oppose more.