The website history.com has a list of some of the most important "checks and balances" put in place by the United States Constitution. Here are some of them and how they are not real checks, they're flawed and easily bypassed by malicious peers that manage to enter the network.
The president (head of the executive branch) serves as commander in chief of the military forces, but Congress (legislative branch) appropriates funds for the military and votes to declare war.
As it has happened multiple times, the United States has engaged in many undeclared wars -- and many other military encounters that don't get enough media coverage and weren't even formally acknowledged by the Congress.
Congress has the power of the purse, as it controls the money used to fund any executive actions.
There's a separate power called Federal Reserve which is more-or-less under the influence of the executive branch that is controlled by a single man and has the power of creating unlimited money. It was softly abused by the executive branch since its creation, but since 2008 it has been increasingly having its scope expanded from just influencing the banking sector to also directly using its money to buy all sorts of things and influence all sorts of markets and other actors.
Veto power. Once Congress has passed a bill, the president has the power to veto that bill. In turn, Congress can override a regular presidential veto by a two-thirds vote of both houses.
If you imagine that both the executive and the legislative are 100% dedicated to go against each other the president could veto all bills, but then the legislative could enact them all anyway. Congress has the absolute power here (which can be justified by fact that the congress itself is split into multiple voters, but still this "veto" rule seems more like a gimmick to obscure the process than any actual check).
The Supreme Court and other federal courts (judicial branch) can declare laws or presidential actions unconstitutional, in a process known as judicial review.
This rule gives absolute power to the Supreme Court over any matter. It can use their own personal judgement to veto any bill, cancel any action by the executive, reinterpret any existing law in any manner. There's no check against bad interpretations or judgements, so any absurd thing must be accepted. This should be obvious, and yet the entire system which most people believe to be "checked" is actually dependent on the good will and sanity of the judicial branch.
In turn, the president checks the judiciary through the power of appointment, which can be used to change the direction of the federal courts
If the president and congress are being attacked by the judicial power, this isn't of much help as its effects are very long term. On the other hand, a president can single-handedly and arbitrarily use this rule to slowly poison the judicial system such that will turn malicious for the rest of the system after some time.
By passing amendments to the Constitution, Congress can effectively check the decisions of the Supreme Court.
What is written in the Constitution can be easily ignored or misread by the members of the Supreme Court without any way for these interpretations to be checked or reverted. Basically the Supreme Court has absolute power over all things if we consider this.
Congress (considered the branch of government closest to the people) can impeach both members of the executive and judicial branches.
Again (like in the presidential veto rule), this gives the congress unlimited power. There are no checks here -- except of course the fact that the congress is composed by multiple different voting heads of which a majority has to agree for the congress to do anything, which is the only thing preventing overabuse of this rule.
As shown above, most rules that compose the "checks and balances" system can be abused and if given enough time they will. They aren't real checks.
Ultimately, the stability and decency of a democracy relies on the majority rule (so congress votes are never concentrated in dictatorial measures) and the common sense of the powerful people (president and judges).
There probably hasn't been a single year in any democracy in which one of these powers didn't abused or violated one of the rules, but still in most cases the overall system stays in place because of the general culture, splitted views about most issues, overall common sense and fear of public shame.
The checks and balances system itself is an illusion. All the complex "democracy" construct depends on the goodwill of all the participants and have only worked so far (when it did) by miracle and by the power of human cooperation and love.