Mrs. Lovett talks, or sings, about how a fellow pie shop owner uses the neighbors cats as meat for her pies. It's because the price of meat is high. You never actually see any cats being killed or used as meat.

The only dogs in the movie are in the background. And they are alive and well.

while the action isn’t shown, there’s multiple mentions of a character killing cats for meat

Mrs Lovett’s entire bakery is crawling with bugs. One crawls out of a pie.

Dogs are only seen walking in the background.

Bug are squashed, and there is talk of cats being baked into pies.

A character mentions cats being made into pies, but it isn't shown.

We are supposed to cheer on the young Anthony who falls for Johanna while she’s staring out her window, but his “love song” is like a stalking anthem: "I'll steal you, Johanna, I'll steal you. Do they think that walls can hide you? Even now I'm at your window. I am in the dark beside you, Buried sweetly in your yellow hair. I feel you, Johanna And one day, I'll steal you." 😳

After Todd beats Pirelli in a contest, he takes his anger out on Toby, a child.

Mrs. Lovett lies to Sweeney, allowing him to think his wife killed herself even though she knows Lucy is still alive. Does that count?

A boy (toby) who grew up in a work house and was taken on my singor Pirelli abuses him quite often with mentions of Lashings and we even see the boy get kicked off a stage and get his hands cut open by a Sharpe blade

To killing, possibly.

The Beadle uses snuff (tobacco that you snort). It's only in one scene and it's brief.

A kid, probably 8-12 years old, drinks alcohol and passes out. An adult gave him the alcohol. Mrs. Lovett give Sweeney Todd alcohol to cope with... Disappoinment

I guess it's not really excessive but the whole plot of the movie is that Sweeney Todd slits peoples throats and they get put into pies. When he slits their throats a load of fake blood is shown and it's kinda obvious that it is fake but it may still be triggering

The whole premise of the movie is of a barber who kills people by cutting their throats whilst shaving them.

The premise is that people are killed, baked into pies, and sold to unknowing customers.

A character is shut in a hot oven and burns to death within seconds. The sequence itself is fairly quick and not extremely graphic but is certainly enough to make some viewers uncomfortable.

We don’t see it but there is a severed finger or a thumb in a pie.

Heads bust when the bodies drop into the basement.

As the kid Toby eats one of the meat pies he finds a cut of finger.

Not on-screen, but a child is convicted of theft and sentenced to be hung.

after throat slitting obviously

One murder is done with many slashes to the throat, causing a slow death.

You can hear bones breaking when the already dead characters falls down the chute to become a pie

Many people fall down a chute after having their throat slit.

A young boy is sentenced to death by hanging but the death isn’t on screen

Sweeney never cheats on his wife. Mrs Lovett fantasizes about the two of them getting married in an imagined musical number, but is clearly completely uninterested in her, even in her imagination

Two. Both on screen.

The judge holds Joanna in his care and even romanticizes her, but I’m not sure if that’s considered kidnapping

No, though a character spits out a good amount of blood.

Sweeney Todd spits out the pie

There's a few sounds that I found a little disturbing, especially the sound of people's skulls cracking when they're dumped down Sweeney Todd's chute.

No, however Bedlam is mentioned.

Theres a mental asylum scene where the patients are very clearly traumatized and abused (tho they eventually get their offscreen revenge)

We are told that Mrs Lovett's husband died due to over-eating.

Not shown on screen, Lucy is said to have poisoned herself.

Few things. Lovett tells Sweeney that his wife Lucy poisons herself, she doesn't die from this, but it's clear she was trying to kill herself and he assumes she does. Also, at the end, Sweeney allows Toby to slit his throat, which isn't technically suicide, but he did absolutely nothing to stop this when he easily could have.

(slight spoiler) a group of women being kept in an asylum attack & kill the man who runs the asylum

A young boy is locked into a rather tight space and is temporarily unable to get out.

Sweeney presumably has PTSD from being in prison for fifteen years. He talks about there being "ghosts" and "shadows" everywhere and lives in the past. His wife also has PTSD, as the other comment mentions

No, but Todd sings about how everyone (including himself) deserves to die.

There are looks towards the camera, but these exist outside of the fourth wall.

There is a baby in Todd's brief flashback, whose pictures are shown in the film, and there is a baby and wife waiting with one of Todd's customers.

Not in the traditional sense, but at one point Sweeney mistakes Johanna for a boy

Todd says there is a considerable amount of fat on a priest.

Johanna is technically judge turpins adopted daughter and he wished to marry her and often made suggestive actions like peeping through her keyhole

It is a very short scene and it doesn't show much but it is implied that Sweeney Todds wife was r*ped.

Implied rape, though not shown in details. And somewhat graphic talk about female sex workers around the world.

The ending is not happy, per say, but I wouldn't say it's super sad

While a gun is pulled, it is not used.

It's one of the main parts of the movie, as Todd really wants to kill Turpin, and many are killed before then.