Store all dates in a given date range into a variable

I would take a completely different approach to this. Doing all the date calculations by hand is error prone (there aren't always 31 days in a month, you have leap years, etc). Plus skimming through your code, it's very hard to tell what you're doing (which is a very bad thing).

#!/bin/bash
startdate=20141030
enddate=20141120

dates=()
for (( date="$startdate"; date != enddate; )); do
    dates+=( "$date" )
    date="$(date --date="$date + 1 days" +'%Y%m%d')"
done
echo "${dates[@]}"

This uses the date command to handle all computations, storing each date in the $dates array.

The result looks like this:

20141030 20141031 20141101 20141102 20141103 20141104 20141105 20141106 20141107 20141108 20141109 20141110 20141111 20141112 20141113 20141114 20141115 20141116 20141117 20141118 20141119

If, as you explained in your comments, your end goal here is to find all files modified within a given date range, then saving said range into a variable is pointless. Instead, you can give the range to find directly:

find . -mtime $start -mtime $end

Personally, I would use a different approach. Just create two temp files, one created a second before your start date and one created a second after your end date. Then use GNU find's -newer test to find files that are newer than the first and not newer than the latter.

The tricky bit is getting $start and $end correctly. You could try something like:

#!/usr/bin/env bash

## If you really want to use this format, 
## then you must be consistent and always 
## us YYYYMMDD and HHMMSS.
startdate=20141030
starttime=165800

enddate=20141120
endtime=175050

## Get the start and end times in a format that GNU date can understand
startdate="$startdate $( sed -r 's/(..)(..)(..)/\1:\2:\3/' <<<$starttime)"
enddate="$enddate $( sed -r 's/(..)(..)(..)/\1:\2:\3/' <<<$endtime)"

## GNU find has the -newer test which lets you find files
## that are newer than the target file. We can use this
## and create two temporary files with the right dates.
tmp_start=$(mktemp)
tmp_end=$(mktemp)

## Now we need a date that is one seond before the
## start date and one second after the end date.
## We can then use touch and date to set the creation date 
## of the temp files to these dates. 
minusone=$(date -d "$startdate -1 sec" +%s)
plusone=$(date -d "$enddate +1 sec" +%s)

## Set the creation times of the temp files.
## The @ is needed when using seconds since
## the epoch as a date string.
touch -d "@$minusone" $tmp_start
touch -d "@$plusone" $tmp_end

## At this point we have two files, tmp_start and
## tmp_end with a creation date of $startdate-1 
## and $enddate+1 respectively. We can now search
## for files that are newer than one and not newer
## than the other.
find . -newer $tmp_start -not -newer $tmp_end

## Remove the temp files
rm $tmp_start $tmp_end