Why aren't any advancements being made in physically diagnosing Bipolar and other psychiatric disorders? I was involved in a discussion where somebody had asked if others had thoughts of doing risky things during their manic episodes. Two people commented, including myself. I worried that only relying on a specific set of guidelines established by the diagnostic and Statistical Manual on Mental Disorders fifth edition could lead to disastrous consequences.

Let's say somebody came into a psychiatrist's office. The person has previously read the DSMV and understands the criteria. That person played their cards right to convince the psychiatrist to diagnose them with Bipolar Disorder, when in truth that person might not likely have it at all. Instead, their true motive would have been to get free benzos so they could space out and get high.

On the other end of the spectrum, some people have been misdiagnosed, leading to unwanted and unnecessary medications.

For both of these situations, why can't blood tests and other physical and objective means be used to insure that neither party is in doubt? You can't lie on a blood test or magneto encephalogram, so why not this?
Short Answer

Science is hard, brains are complicated, and the premises of your question that there is not work being done or advancements in this area is false.

Longer Answer

There is no known specific cause of bipolar disorder (as for many other psychological disorders). There is no simple statement like "bipolar disorder happens when you are low on XYZ so let's test for XYZ." Bipolar disorder and many others are in fact defined by the DSM based on symptoms - diagnosing them in another way is not the gold standard.

That said, you seem to be implying especially in your comment "why isn't one being developed" that this isn't an active area of research. It is - a helpful search term for you will be 'biomarker'; Google Scholar returns 4,480 results since 2017 for ("bipolar disorder" "biomarker").

However, all of the suggested biomarkers are some combination of A) Not specific (i.e., are positive for other conditions), B) Not sensitive (i.e., are negative for people that do have bipolar disorder), C) Expensive or invasive (i.e., not really worth doing if they have issues with A and B), or highly dependent on other individual factors.