Well, there is undoubtedly some crime that must have slipped through the various police forces of the world, indeed, but not that much, especially in the 19th century.

You say "poor policing techniques", but what you describe as an exemple is not properly speaking a "police technique", but rather a "scientific policing technique". Police technique is the way you handle a possible crime and start an investigation. In the case of a poisening, it's not so much the exact nature of the poison used that is determinant, but rather the circumstances of the death : were the victim healthy or not, did he collapsed suddenly, who cooked the food, who were here at the time of death... Today, an autopsy is mandatory in most countries. In the 19th century, it was less common, but already used if the police suspected fowl play.

 

But most importantly, your question is about the crime rate. And the inability to SOLVE a crime doesn't mean this crime is not accounted for. I studied law enforcement in France in the 19th and 20th century for my degree, so my anwser stend mostly for France, but is, more or less, applicable to most European country in this periode. In France, police was handle mostly by two corps in the 19th century : The national Gendarmerie, and the municipal police, only present in the major cities (national police is only created in the 20th century). These two corps have various statutes over the course of the 19th century, because the political system change about every 20 years in France during that time periode, but overall, their missions don't change : Gendarmerie handles crimes all over the country, municipale police crimes in the major cities. There would be a lot to be said about the history of gendarmerie and police, but that not the subject here, so I will leave it to that brief summery for now.

Both this corps produced A LOT of paperwork. Every incident is the object of a police report and minutes if someone is interrogated. Of course, it's reasonnable to assume that agents sometime skip the paperwork for minors incidents, but the archives we have allow us to think that the agents are quite serious, because we have a lot of trivial - and sometime funny - report about little everyday incidents (a drunk that made a mess, a farmer that didn't had a lantern on his carriage, as the law require...). So we can be pretty much sure that, when someone dies in dubious circumstances, they are not going to skip on paperworks.

And as I said, for having seen the archives, there is a lot of paperwork. Some of it is lost, of course, but what we still have most of the reports and minutes, kept by the police prefectures and the gendarmerie's archives. We have a pretty define idea of the crime rate, the nature of crimes and how frequent they were. Even if most of them are indeed not solved.

 

I would add that we can detemine the crime rate through another source, wich is the press. Press, in the 19th, contains a lot of publication about crimes and criminel, because this kind of news is good for selling papers. There is reporters that specialise in following police investigation, that keep many contacts and informer inside the various polices forces, and account for crimes, especially murder and gruesome affairs. Of course, these sources are bias, tend to emphazis crime spreas and so on, but, when crossed reference with police archies, allow us to make a quite accurate representation of the crime rate at a given time.

 

So [TL;DR] ; No, the lack of scientific police and advance investigation techniques in the 19th doesn't affect our knowledge of the crime rate very much. It affect, however, our knowledge of criminal as individual, since a lot of cases are not solved.

 

If the subject of police investigation and crime in the 19th century France interest you, the main author on the subject is Dominique Kalifa, a french historian. Infortunatly, most of his books (especially L'Encre et le sang, a fascinating studie on crime and press at La Belle Epoque) are not translated in english. But you can find some articles he wrote in english, that constitute a good introduction on the subject, and will probably reference some english authors on the subject.

If you want to read on that from the point of you of law enforcement, the main author in France is Jean-Noel Luc (who was my director of research for my degree), but like Kalifa, you can only find article by him in english, his books being only published in French.