Two approaches to Olam Haba

סנהדרין דף קיא ע"א

"לכן הרחיבה שאול נפשה ופערה פיה לבלי חוק"
אמר ר"ל- למי שמשייר אפי' חוק אחד
אמר לו יוחנן- לא ניחא למרייהו דאמרת להו הכי אלא לא למד אפילו חוק אחד

  

Sanhedrin 111a 

"Hell shall widen its mouth and swallow those without Law" (Yeshayahu 5:14)
Rish Lakish said: Hell swallows those who neglected even a single Law.
Ribbi Yochanan told him: God doesn't appreciate that you judge His people so harshly. Rather, the pasuk means as follows- Hell swallows up only those who wouldn't even observe a single Law.

A"A says that we see here two distinct approaches to olam haba. In Rish Lakish's paradigm, Hell has an all-or-nothing nature. If you screw up once, you're out of the race. Ribbi Yochanan flips it. Observing even one mitzvah is enough to keep you out of Hell.
As we have discussed previously, the Rambam's approach (as presented in Perush Hamishna Makot 3:17) is consistent with Ribbi Yochanan.

(It is worth noting that all this is only relevant when discussing God's account of our observance. Between man and his fellow, those who outright reject even a single mitzvah of the Torah are given the halachic status of "meshumadim" (Rambam Hil' Teshuva 3:9).)

Prophecy and Psychosis

בבא בתרא דף יב ע"ב  

א"ר יוחנן מיום שחרב בית המקדש ניטלה נבואה מן הנביאים וניתנה לשוטים ולתינוקות

Bava Batra 12b

Ribbi Yochanan says: Since the day that the Bet Hamikdash was destroyed, prophecy was taken away from the nevi'im and given instead to the psychotic and small children. 

A"A says that if anyone ever claims to you that he received a prophecy, you can be confident that he is either lying or mentally ill. 

Selective Babylonians and their dating habits

קידושין דף עא ע"ב

זעירי הוה קא מישתמיט מיניה דר' יוחנן דהוה אמר ליה נסיב ברתי יומא חד הוו קאזלי באורחא מטו לעורקמא דמיא ארכביה לר' יוחנן אכתפיה וקא מעבר ליה א"ל אורייתן כשרה בנתין לא כשרן מאי דעתיך אילימא מדתנן עשרה יוחסין עלו מבבל כהני לויי אטו כהני לויי וישראלי כולהו סליקו כי היכי דאישתיור מהני אישתיור נמי מהני אישתמיטתיה הא דאמר ר"א לא עלה עזרא מבבל עד שעשאה כסולת נקייה ועלה 

Kiddushin 71b

Zeiri would constantly avoid Ribbi Yohanan's pleas to marry his daughter.  One day they were on the road together and came to a river that was blocking their route. 

"Hop on my shoulders and I'll carry you across!" Zeiri said to Ribbi Yohanan (who was apparently a weak swimmer). 

"Why all the respect?" Ribbi Yohanan asked him. "My Torah is good enough for you but my daughter isn't? Do you think that your yichus is better than mine just because you're from Bavel and I'm from Eretz Yisrael?"

Ribbi Yohanan forgot about Ribbi Eliezer's statement: "Ezra didn't leave Bavel until he sifted it thoroughly and removed all the pesulim and took them with him to Eretz Yisrael." 

We see from this Gemara how careful they were back in the day about yichus. A"A pointed out that Ribbi Yohanan was extremely good looking according to the Gemara (Berachot 20a) and its reasonable to assume that his daughters were probably hot too. But Zeiri was still careful not to marry into his family because they weren't Babylonian.