I have been experimenting with 165, e.g. 74HC165, to increase inputs. When I first started out with it, I simply grounded any unused pins (breadboard). I am aware that using a single 165 means you only increase the inputs by 5 for the first device, because you need 3 pins on the Arduino anyway. For any subsequent linked 165, you do indeed get another 8 inputs.
I am maybe thinking (in terms of my initial question) of if the chip was soldered onto a shield/ stripboard etc. This takes into account soldering fatigue of the stripboard (I may be using the wrong word, in that I mean the stress on the stripboard due to de-soldering and resoldering). If it is on a breadboard then there is the awkwardness of having to use jumpers to ground unused pins. However, it is not too much effort or waste of ground space on the breadboard. Maybe even that is not necessary though!
So, if those inputs are irrelevant, and unused, does it have any undesirable effect on the whole circuit if they are not grounded, and floating? Can you just leave them for now (i.e. floating), with the intent of including extra ones at a later stage, if needed? I have found stripboard can be a little flimsy regarding de-soldering/ resoldering.
What if you leave unused pins floating? Does it have any negative effect, if they are just unused?
Always check the device data sheet. It is your very best and most reliable source of information.
(1) All unused inputs of the device must be held at VCC or GND to ensure proper device operation. Refer to the TI application report,
Could this mean that the shifting nature of the device may imply instability in the other input pins? Therefore, maybe it could adversely affect the other pins on the chip?
I am maybe thinking that the exact shift processing nature of the whole program would indeed cause interference!
If I remember my electronics correctly.
Floating inputs toggle. As a result the internal electronics of an IC associated with a floating input will switch; this will result in higher current consumption.
IF you want to keep it flexible you can use pull-up or pull-don resistors on the inputs of the 165.
Floating inputs are almost always a major problem, for several reasons. As mentioned above, they toggle randomly, usually due to electromagnetic and atmospheric (EMI and stray charges) influences.
Oh, for one thing, I would be using pull-downs, on the switches themselves, because I would unlikely be using 3 pin switches. I use pull-down instead of pull-up, because the semantics mean you do not need to use an inverter chip. I am very much in favour of DOWN rather than UP due to it not being directly programmable. I believe pull-up is default for Arduino, because you can simply invert, and use LOW instead of HIGH, in the IDE programming.
Yes, indeed. That was one thing I was worried about due to unwanted activity.
Pulldowns are built in and programmable on many modern MCUs. The ATmega328x on the Arduino Uno R3 was designed over 30 years ago.
I do believe, if I am right, things like Nano or UNO, only have PULLUP. I seem to remember reading they simply do not have the PULLDOWN as an option for programming. For that reason switches have to be inverted due to this.
Check the device data sheet, then you don't have to guess.
When I was referencing INPUT_PULLUP I was only referring to the ARDUINO IDE programming platform, with use of the internal PULLUP resistor. I have familiarized myself more with the use of using a breadboard , and adding in the resistor myself, and then simply using INPUT. A lot of the time I do simply use INPUT_PULLUP, and then just state LOW instead of HIGH in the program. Because I am using 165 for inputs, I find that I have to do it physically, on the circuit.
I have made stripboard shields for the little pushbuttons that come with project packs now. They are unreliable if you use them directly on the breadboard because they pop out of the board 
Not necessarily!
SW1 in Fig-1 works fine with Rip of the MCU.
Figure-1:
The Arduino IDE platform can also be used to program MCUs that have internal pulldowns.
For example, here are instructions for the ESP32:
When using some of the base-line logic chips, you do end up finding that things are inverted anyway. If my memory serves me correctly, I found this with the 3-8 converter 74HC chip. Whatever the number was 
I think that may be one of the ones I found a use of the inverter logic chip for.
Ah, OK jremington, I will have a look at that, thank you!
Are you talking avout 3-to-8 decoder -- 74HC138? You can connect the output directly with an input pin of the MCU with Rip enabled or disabled.
GolamMostafa, I may have been using it raw, rather than using an MCU. I bought some chips to experiment with, and avoided using the Arduino, to get familiar with baseline logic chip usage. I found it a lot of fun to try things without the use of an MCU, and just switches. I did similar things with 555, to familiarize myself with core usage of chips.
Yes, indeed it was 138 I was referencing. I believe that was the one I found a use for the inverter 04 chip! Due to my inexperience I thought the NOT-GATE chip, 04, seemed weird, but then I realized its use.
If you iterface your base line logic with MCU, you can do a lot of fun. For example: driving a STOP Watch (Fig-1) using 74HC595.
figure-1:
You’ve got the spirit! So many things you can just play with. We all saw all these little electronic bits and pieces as a child, and all of a sudden you can just work out how they worked. I love it!