The iPhone 4S came with iOS 5. My current iPhone 6 is running iOS 9.3.5. After I publish this post, I will upgrade to iOS 10 and retest all the bugs and discrepancies and look for the desired features and update this post if there are changes. Some of these may be fixed already as some of them are hard to test with iOS 9.
Many of these bugs and discrepancies go back to iOS 5. I don't understand why they don't get fixed. I can't be the only one out of millions of users who has noticed these problems.
I'm only discussing applications and the keyboard provided by Apple as part of iOS.
Phone and Contacts
When a contact is marked as "Blocked" and you add a phone number to that contact, the added phone number will not be blocked. You must unblock and block the contact again to begin blocking the added phone number.
The "1" digit on the phone keypad is tricky. I've had cases where I needed to dial the "1" but was unable to do so. Many times, the screen just flashes. When I have a conference call and the authorization code includes a "1", I set it up in Contacts so I can dial the number from Contacts and avoid having to try to dial the "1". This seems to have improved and it may be finally fixed.
If a call comes in as "No Caller ID," you can't set up a contact for it and mark it as blocked. Your phone will ring every time (unless you have turned the ringer off for all calls).
If your voice mail is 100% full, the app won't show you this until you go into voice mail.
Desired feature: When a call comes in and on the list of recent calls, the name and type of call shows up. I would rather have the name and company name show up. Sometimes, I don't remember what company a person is associated with.
Desired feature: If I'm in an app when the phone rings, I can accept or decline the call. I want to be able to do this when I'm on the home screen. I can mute the ringer, but I can't decline the call. If I put my phone back in my pants pocket, I run the risk of accidentally answering the call.
The Weather app is atrocious and I'm surprised that The Weather Channel allows its logo to be included. It's especially interesting to watch the app update the forecast to the actual as you go through the day. For example, at 10 a.m., it might say the temperature is 60º at 10 a.m. but that it will be 75º at 11 a.m. No it won't.
Most days, the high temperature for the day is higher than the highest hourly temperature.
The Weather app requires that you turn on location tracking even when the app isn't being used. Why are you spying on me and using up my battery?
Desired feature: Include the humidity with the temperature. Especially in the summer in Ohio, the humidity can have a major influence on the perceived temperature.
The prediction capability of the keyboard is helpful yet infuriating. I don't like it when it takes perfectly valid words and changes them into invalid words. I thought it learned my vocabulary but I seem to be mistaken as I have to correct it over and over again for some words, especially slang.
When I type "a.m." or "U.S.", the keyboard turns capitalization on after the period even though I the next letter is not capitalized 90% of the time. Example: "I will leave at 4:45 p.m. and head home." The "a" on "and" should not be capitalized but it will try to capitalize it. It should monitor my typing and turn the capitalization on only when I'm at the end of a sentence.
Desired feature: If I type a number, then a space, the keyboard returns to showing letters instead of numbers. I want it to stay with numbers.
When I see a full message through the Notification Center or just from the list of messages, the unread message indicator is not cleared. I have to go into the actual message to clear the indicator even though I have already read it. This is especially annoying when the message is "K".
Sending a message with a picture is weird. If I click on the camera icon first, I can now add a message to the picture (this was added at some point in iOS 9). If I enter the message before clicking on the camera icon, the message will not be sent with the picture.
General User Interface
The icon used to add an item to a list of items is not consistent. The Stocks, Contacts, World Clock and Calendar apps uses a + sign, which is what I would expect. However, Notes and Messages use a box with a pencil instead. The Weather app uses a + in a circle to add a location.
The search box is normally shown on apps that have a search capability, such as Safari. However, Notes hides the search box until you scroll. It doesn't take up much space, so it should always appear.
I was watching Apple stock one day when the price changed dramatically. I noticed that the dividend yield was not recalculated as the price changed.
Desired feature: There needs to be an API that an app can use to determine if I've written a review for the app. Some apps ask me to write a review when I have already done so. I find this annoying.
Desired feature: When I look at purchased apps, they seem to be listed by the most recently installed to the earliest installed. I would also like a list in alphabetic order so that I can find a desired app quicker.
Desired feature: Unlike the Chrome browser for the iPhone, you can't search on a page for a word.
That sums it up. Feel free to use the comments for corrections or additions.