A few points to consider.. Yes, there are circumstances where you can search without a warrant (but you'd better be reasonable and have solid circumstances to back you up...) and have it good in court later. Most homicide investigators that I knew far preferred to get a warrant if at all possible since a warrant issued by a judge is far more likely to stand up in court... I even saw instances where at a homicide scene the killer left his (or her) firearm visible inside a locked car - and yet the investigators carefully secured the vehicle and waited until a judge issued a search warrant before entering the vehicle... In serious cases you always wanted to be as solid with evidence as possible since a key piece of evidence that's later tossed out can sink a case entirely... The main problem that I saw on the street was that everyone watches all the cop shows on TV or in the movies - and I rarely ever saw an accurate version of the laws regarding search and seizure on the tube (or on the screen...). That's why anyone in a possible criminal case is well advised to have a lawyer (and a lawyer that actually handles criminal matters...).
As far as dogs go - our SRT had a specific officer whose job it was to "kill the dog" if necessary... Let me back up and point out that most of the time we simply brought an animal control officer with us and it was their job to secure the dog (without injuring it - using a catchpole... ). We also made a point of scouting the structure before acting and very carefully briefed the entire team before the fact since a door that doesn't open the way you expect it to might end up getting someone killed... and knowing whether there were animals on the scene was also important... In a few cases the bad guys deliberately placed vicious dogs or other living hazards at their door or in their yards to prevent or delay a warrant service (usually drug dealers - or folks involved in explosives or weapon violations... ). Their idea was to use the dog(s) to delay entry while they were either destroying evidence or arming themselves or trying to evade arrest... Very bad scene... and very dangerous to officers and anyone else at that location. The result - a dedicated officer with a short barreled shotgun - and adios Fido... It should be noted that in my experience shooting one dog will seriously discourage the others - or at least get them to back off until you could secure the scene (or get the owner to properly secure the dogs..). Most of our guys were dog owners themselves and never sought to "kill the dog" - but sometimes it was a very necessary action. Have tragedies and mis-carriages of justice occurred in these types of incidents? Absolutely, but very few that I ever knew of...
For honest folks, my best advice is to be careful of any friends or family involved in criminal activities since their very presence in your house escalates the chances that police action will end up where you live... When I was a young man, fresh back from Vietnam all those years ago, long before I entered police work - I never even thought about that. It was not uncommon back in the early seventies to walk into someone's house and see a pound of grass on the kitchen table (south Florida was pretty much wide open in those "Jimmy Buffet" days). I was in places and knew folks back then that would later end up going down for everything from murder on down... and could have very easily been in the wrong place when a raid or warrant service went down... Something to think about when you have kids or your own - or in my case grandkids... Make sure you caution them - and of course you can be certain they'll ignore you... At least that's what I did - all those years ago..
Excellent summary above.
When training new deputies, I always had them closely review, and made sure they fully understood, the U.S. Supreme Court's decision in Mincey v Arizona. That case explains why your homicide detectives were so careful to get a warrant. In the Mincey case, a Tucson undercover officer went to Mincey's apartment to buy dope. Something went wrong and there was a shooting between Mincey and the officer. Mincey was wounded and the officer killed. Backup officers entered the apartment, summoned medical aid for the officer, and arrested Mincey. Detectives and the crime lab folks arrived and did a full crime scene work-up. Mincey maintained at trial that he shot the officer believing him to be a drug dealer who was attempting to rob him. The prosecution successfully impeached Mincey's testimony by showing the trajectory of fired rounds was inconsistent with his version of events. Mincey appealed claiming that a search warrant was need for the crime scene work-up. The prosecutor argued that Arizona law provided a "crime scene" exception to the search warrant rule, and that officers made lawful entry to the apartment due to the exigency of the shooting. The Supreme Court overturned Mincey's conviction holding that while the initial entry was justified as an exigency, the crime crime scene work-up was not. Once the injured parties were removed from the scene, the exigency (and the corresponding search authority) ended. The Court also found that Arizona's "Crime Scene" exception violated the Fourth Amendment.
I made it a point to emphasize Mincey because LEO's tend to get into a "flow of activities" at emergent scenes and often don't realize that the legal "scene" changes considerably when the emergency passes.
At one point, I had a very minor question about the case that wasn't addressed in the decision. I called the D.A.'s Office in Tucson to get some more background as was put in touch with the actual prosecutor in the original case. I only planned on a five minute call at most, but spent three hours on the phone, and it wasn't me dragging out the conversation. Mincey was re-tried (without the crime scene evidence) and the jury hung in the second trial. He was tried a third time and was ultimately convicted.
I also share the above comments about dogs. I've responded as a supervisor to many cases where deputies have shot dogs, and it was never a "family pet" that was shot (even though it was often presented that way in the press). It was typically a "Guard Dog" that was tasked with guarding the illegal operation that deputies were responding to. In one case, the dog survived a .45 round. It's owner later boasted to his fellow gang members that the shooting showed how tough his dog was, and that the dog shouldn't be messed with.
I'm a big believer in the use of search warrants, and another point that I often made when teaching new deputies is that taking the time to get a search warrant gives the LEO ownership of the legal "Gray Area" if the search is later questioned in court. It works like this - A search conducted under an exception to the search warrant requirement is presumed to be unlawful and the prosecutor has to show it lawful in order to admit the resulting evidence. A search conducted with a warrant is presumed lawful, and the defense has to show it unlawful in order to exclude the evidence. In the real world, no showing of evidence is perfectly "good" or "bad". There are the two extremes and then a big "Gray Area" between them. If I do a search without a warrant, and the court finds it in the "Gray Area", I lose my evidence. If I do the same search with a warrant, and the court finds it in the "Gray Area", I keep the evidence. That's a big advantage. At the same time, the burden of proof shifts from the prosecutor to the defense to show the unlawfulness of the search. That often requires the defense attorney to play cards, they'd rather hold in order to win on a motion to suppress the evidence.