Things not to mix

TL; DR - The first two are bad. The third and fourth are very minor worries.

I came across this graphic online and thought I'd take a moment to check the chemistry involved.

Let's go in order, and I'll cite sources as I find them...

From ThoughtCo.com...regarding bleach + vinegar

What Happens When Bleach and Vinegar Are Mixed 

Chlorine bleach contains sodium hypochlorite or NaOCl. Because bleach is sodium hypochlorite dissolved in water, the sodium hypochlorite in bleach actually exists as hypochlorous acid: 

NaOCl + H₂O ↔ HOCl + Na⁺ + OH^-

Hypochlorous acid is a strong oxidizer. This is what makes it so good at bleaching and disinfecting. If you mix bleach with an acid, chlorine gas will be produced. For example, mixing bleach with toilet bowl cleaner, which contains hydrochloric acid, yields chlorine gas: 

HOCl + HCl ↔ H₂O + Cl₂ 

Although pure chlorine gas is greenish-yellow, gas produced by mixing chemicals is diluted in air. This makes it invisible, so the only way to know it's there is by the smell and negative effects. Chlorine gas attacks mucous membranes in the eyes, throat, and lungs—these attacks can be deadly. Mixing bleach with another acid, such as the acetic acid found in vinegar, yields essentially the same result: 

2HOCl + 2HAc ↔ Cl₂ + 2H₂O + 2Ac^- (Ac : CH₃COO) 

There is an equilibrium between the chlorine species that is influenced by pH. When the pH is lowered, as when adding toilet bowl cleaner or vinegar, the ratio of chlorine gas is increased. When the pH is raised, the ratio of hypochlorite ion is increased. Hypochlorite ion is a less efficient oxidizer than hypochlorous acid, so some people will intentionally lower the pH of bleach to increase the oxidizing power of the chemical even though chlorine gas is produced as a result.

So, I'd say that one checks out.

Next up, bleach and ammonia...again, from h2g2.com...

When these two compounds are combined, the following reaction takes place:

2 NaOCl + 2 NH₃ --> 2 NaONH₃ + Cl₂

...

Another potential reaction, which occurs when a greater amount of bleach is added than ammonia, is this:

3 NaOCl + NH₃ --> 3 NaOH + NCl₃

That's sodium hydroxide and nitrogen trichloride. Nitrogen trichloride is a very toxic chemical to humans, and even if you did get close enough to ingest it, it would probably explode in your face first, as it is also a very volatile explosive.

...

Still another reaction - in three parts this time - can occur, producing hydrazine, N₂H₄, a component of rocket fuel) if you have more ammonia than bleach:

NH₃ + NaOCl --> NaOH + NH₂Cl

These two products then react with ammonia as follows:

NH₃ + NH₂Cl + NaOH --> N₂H₄ + NaCl + H₂O

One last reaction occurs to stabalise the reagents:

2 NH₂Cl + N₂H₄ --> 2 NH₄Cl + N₂

That last equation is of particular interest because of the amount of heat it produces. The heat is so great that it usually leads to an explosion.

Again, I'm okay with staying you definitely shouldn't mix those two. I did, however, struggle to find a source with reactions that I trusted. The first two I found - this and this - didn't make sense in a few places, having missing mass in various places in their reactions.

Now, bleach + rubbing alcohol...

I'm a little less sure about this one. I found a lot of sources that say this one produces "chloroform, (CHCl₃), hydrochloric acid (HCl), and other compounds, such as chloroacetone or dichloroacetate." but I can't find the exact chemistry anywhere.

The only reaction I could find, however, in all of the articles was of acetone with bleach.

3 NaClO + C₃H₆O --> CHCl₃ + 2 NaOH + NaOCOCH₃

Acetone and isopropyl (rubbing) alcohol certainly aren't the same thing. So I'm going to leave this one as a maybe as I also found a fair number of sources that said any reaction between isopropyl alcohol and bleach would be fairly slow and likely would need a catalyst to see significant product production at room temperature.

The last combo is hydrogen peroxide with vinegar (acetic acid). From wikipedia...

[Peracetic acid] forms upon treatment of acetic acid with hydrogen peroxide with a strong acid catalyst.

H₂O₂ + CH₃CO₂H ⇌ CH₃CO₃H + H₂O

From cooksinfo.com

If you mix the two together in one bottle, a weak form of peracetic acid is formed. Peracetic Acid ( aka peroxyacetic acid) is a mixture of acetic acid and hydrogen peroxide. Peracetic Acid is primarily used for deactivation of a large variety of pathogenic micro-organisms in the industrial food industry, medical supplies and to prevent biofilm formation in paper pulp industries. It is usually produced in concentrations of 5 – 15%. This industrial formulation is toxic by inhalation, ingestion or if absorbed through skin; caustic and corrosive at concentrations > 10%; irritant at concentrations below 2%. Retail vinegar is a mixture of acetic acid and water composed of 4 to 8% acetic acid. Hydrogen peroxide at 3 % and retail versions of vinegar are an extremely diluted form of peracetic acid. Mixing the diluted form of acetic acid (known as vinegar) with 3% hydrogen peroxide forms a weak form of peracetic acid that may cause some reaction to those who are very sensitive to it – another reason, besides effectiveness, that applying the two solutions separately is recommended.

So this one I'm going to say is true but a minor issue.

Seriously, though, the first two combos - bleach with either vinegar or ammonia - are bad combos and are to be avoided. The other two, maybe less so...maybe.