Well let's face it, the Eurovision Song Contest is a song contest (a kind of competition). It is not a museum. Since the debut ESC in 1956, the Contest has been continually changing in some way or other. Some changes have been necessary due to new countries from old ones (e.g. break-up of Yugoslavia), and the ever-growing number of countries eligible / wanting to enter (relegation, semi-finals etc). No doubt some changes that have occurred over the years have been controversial.
1) The very first ESC in 1956 had just 7 countries, but each country had 2 songs. In 1957 each country was limited to just one song, it's been like that since. Presumably right back then the organisers anticipated more countries would want to enter each year and it would therefore be necessary to limit each country to just one song.
2) The scoring in 1957 was kept until 1961. From 1962 to 1966 three different systems were tried, but for some reason they never caught on. So from 1967 to 1970 they went back to the 1957-1961 system. In 1971 a new system was tried, in which it was impossible to finish on nul points, but that was used for only 3 years. After a return to the 1957-1961 system in 1974, the 1, 2, 3, 4, 5, 6, 7, 8, 10, 12 points system was introduced in 1975 and has lasted until this day.
3) Israel debuted in 1973 and first won in 1978. I've read somewhere some argued at the time that Israel shouldn't enter the ESC as it's not in Europe.
4) Relegation was introduced in 1993, i.e. a certain number of the lowest placed countries in 1993 had to sit out the 1994 ESC to accommodate new countries in 1994. The same happened at the end of the 1994 ESC, lowest placed countries out of the 1995 ESC to let the 1994 absentees back in.
5) In 1996 the low-placed countries from 1995 who would have had to sit out the 1996 ESC got a chance after all, but those forced to sit out 1995 didn't get free entry either! Instead there was an audio only pre-selection qualifier (not broadcast in any way), and only the top 22 countries joined hosts Norway for the 1996 ESC. Only used once.
6) 1997 - 2000 saw relegation used again, based on the last 5 years placings. This made it difficult for some countries like Lithuania to build up a record. Interestingly Lithuania who came last with nul points in their debut year 1994 didn't appear again until 1999. Were they given a free place in 1999 as they hadn't had chance to build up a record? Someone I knew at the time felt relegation was unfair and a semi-final would be better.
7) Circa 1999 it was announced that from 2000 the UK, France, Germany and Spain, all of whom pay most into the EBU, would get guaranteed entry each year no matter how badly they've done the previous year, i.e. the start of the Big 4 rule. The person I knew whom I mentioned in the previous paragraph felt it was unfair that these countries should be exempt from relegation.
8) This was modified again in 2001; only the Big 4 + top 15 of the rest went on to 2002 ESC, the rest had to sit out the 2002 ESC. The same rule was used for 2002 into 2003.
9) In 1999 were allowed to sing in any language, that stands to this day. Many then sang in English (which some like, some don't like). Belgium tried the novel approach of a made-up language in 2003.
10) From 1999 there was no requirement to provide an orchestra, and that year's host broadcaster IBA (Israel) didn't have one. Another controversial move, Johnny Logan commented that the contest turned into "karaoke" as a result.
11) Televoting was piloted in a few countries in 1997, most countries used it in 1998 and I think it was mandatory by about 1999 or 2000. In 2009 they changed it again to 50/50 jury and televoting.
12) By 2004 there were so many countries eligible to enter it was necessary to have a semi-final for the first time. The Big 4 plus 10 best of the rest from 2003 were automatically in the 2004 final, the top 10 from the 2004 semi-final got the remaining 10 final places. This was used until 2007.
13) In 2008 the EBU decided to have two semi-finals (which I think is fairer). Only the host + Big 4/5 get automatic places in the final, the top 10 from the semi-finals fill the remaining final places.
14) Only solo artists were allowed in 1956, duets were allowed later, and in 1971 groups of up to 6 were allowed for the first time.
15) In the early days there were no age restrictions on participants. That saw 13 year old Sandra Kim win for Belgium in 1986 (youngest ever winner), and youngish children appear with adults in certain 1970s / 1980s songs. In 1990 the new rule stating you had to be at least 16 was introduced.