Understanding reasonable suspicion with DUI
If an officer wants to stop you, they must have "reasonable suspicion" that you either broke a traffic law, or that you are engaged in criminal activity. A "bad" DUI stop is when that officer has lack of reasonable suspicion and stops you for a DUI anyway.
In the vast majority of DUI arrests, the stop takes place because of an alleged traffic violation. May be something obvious as speeding, or subtle, at nightime not having properly lit license plate, or making wide turn.
As long as you don't live in a fantasy world or a bubble. Your probably well aware that officers sometimes make up a traffic infractions. This is in order to stop you to see if you've been drinking. To see the truth of this assertion, somebody could request the records from all traffic stops during a given year. To bet virtually any sum of money, there are vastly more "wide turn" and "weaving" stops at night, than daytime.
Think about it. Do you know many people who received daytime citations for making right turns into middle lane instead of curb lane? The answer is probably "zero."
If the police do not suspect criminal activity before the stop. Then they arrest you for DUI without having or making up reason to stop you for a traffic law violation. They then lack reasonable suspicion to stop you.
Reasonable suspicion in relation to the courts
In order for a judge to declare a warrant-less stop leading to a DUI arrest valid, the police will have to establish that they were not acting randomly or in "an arbitrary manner," and that they weren't simply stopping you to mess with you or harass you.
Once the police stop you, they will have to justify the manner and the length of time that they hold you. In a DUI case, if an officer pulls you over for a traffic violation and then smells an odor of alcohol or notices other indicators that you have been drinking, most courts will find that it is reasonable to detain you long enough to make a determination as to whether you are under the influence of alcohol or drugs. Typically this is long enough to do field sobriety testing, breath testing, or blood testing.
There is no magic formula to determine whether your case might have a viable motion to dismiss for lack of reasonable suspicion. Each case must be decided on a case by case basis. It is not always wise to bring this type of motion in every case. Therefore, you should always consult with a local experienced DUI lawyer to determine the merits of your case.